Is the weighted sum of two normal distribution PDF's also a normal distribution?

Intuition for why sum of gaussian RVs is different from gaussian mixture


Why according to distribution graph it's normally distributed, but Jarque-Bera test shows non-normally distributed?

If my histogram shows a bell-shaped curve, can I say my data is normally distributed?


Correlation between a nominal and ordinal

Correlation coefficient between a (non-dichotomous) nominal variable and a numeric (interval) or an ordinal variable


In an observational study in causal inference, why are the covariates usually assumed to be iid? What happens if they are not?

In the superpopulation framework of causal inference, what is the necessity of assuming the outcomes, treatment and covariates are jointly iid?


Does the "No Free Lunch Theorem" apply to general statistical tests?


Why R is not significant (and very low), while all predictors are significant?

Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic


Why is the rescaled sample SD Chi distributed?

Why is the sampling distribution of variance a chi-squared distribution?


t test with drastically different sample sizes

Independent samples t-test with unequal sample sizes


Does higher AIC correlate with higher adjusted R squared?

When AIC and Adjusted $R^2$ lead to different conclusions


Distribution of $1/\sqrt{X}$ when $X$ is a gamma variate

Square root of an inverse gamma distributed random variable


If A is independent of C and B is independent of C, is their conjuction also independent of C?

If $A$ and $B$ are independent events, and $A$ and $C$ are independent events, how do I show that $A$ and $B\cup C$ are independent?


Binary Logistic Regression using Non-Dichotomous Independent Variables; SPSS

Coding categorical variables for regression


What is a "good fit" Brier score and Harrell's C Index


Probability Interval for Gamma Distribution


why is the standard error so high for my probit model


Square of a normally distributed variable

Distribution of the square of a non-standard normal random variable


How to transform a dataset so that it has a given mean and standard deviation?

Transform Data to Desired Mean and Standard Deviation


How to obtain the Gaussian conditional pdf, as discussed in section 2.3.1 in Pattern Recognition and Machine Learning, Bishop?

Interpretation of multivariate conditional gaussian function form?


Why over/under-sampling could not help my model fitting?

What problem does oversampling, undersampling, and SMOTE solve?


Interpret the comparison between conditional probabilities of the same random variable but different conditions

What is the meaning of p values and t values in statistical tests?


Exactness of p-value in testing by simulation

Confidence interval for the p-value estimate when doing Monte Carlo testing


When doesn't the chi-squared statistic follow the chi-squared distribution?


Interpretation of R's output for binomial regression


Why the CDF for the Normal Distribution can not be expressed as a closed form function?


Bimodal univariate distributions are always indicative of a mixture of two random variables. Is this correct?

Why are all known distributions unimodal?


Is chi-squared necessary if comparing entire populations?

Does it make sense to compute confidence intervals and to test hypotheses when data from whole population is available?


How to obtain t-value for significance of median


Limiting distribution of MLE when true value is on the boundary of the parameter space

General theorems for consistency and asymptotic normality of maximum likelihood


Report coefficients of a factor in a GLM

Interpreting coefficient in GLM with categorical explanatory variables


Prove that $t_{n-1, \alpha/2}$ is strictly decreasing in $n$


linear regression in statsmodel.formula.api python

Linear Regression makes impossible predictions


Detecting outliers in time-series if I don't have a "normal" dataset

Outlier Detection on skewed Distributions


maximum likelihood : why log of function gives maximum value

Validity of maximising log-likelihood for maximum likelihood estimation


What does asymptotic significance value less than 0.95 tells when results are already significant with 0.05 value?

What is the meaning of p values and t values in statistical tests?


Analytical distribution of $N$ standardized samples?


comparing Pearson Correlation of 2 samples against a rating sample set

How to compare two Pearson correlation coefficients


How to decide if Central Limit Theorem is applicable on a sum of Poisson variables?

Normal approximation to the Poisson distribution


Interpreting a binomial regression model in R with cloglog link function

interpreting estimates of cloglog logistic regression


ARIMA: no trend, no seasonality, so what is there to forcast?

Why is removing instationarities a good thing when trying to forecast a time series?


Why is the interaction term defined by multiplying the IVs?

Moderated regression: Why do we calculate a *product* term between the predictors?


Sampling from multivariate normal using a pseudo-inverse

Generating samples from singular Gaussian distribution


Why neural network does not learn sparse relationship

Why doesn't regularization solve Deep Neural Nets hunger for data?


Trend & Seasonality Determination in Time Series without looking at Graph

Period detection of a generic time series


How can I generate 2 sets of variables from different distributions with a correlation between them in r?

Generate a random variable with a defined correlation to an existing variable(s)


Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?


Evaluating mediator effect, through SEM model selection with AIC

Can the likelihood ratio test be used to test mediation?


Conflicting approaches to variable selection: AIC, p-values or both?


Paired t-test for repeated measurements, but with 2 missing samples.

t-test for partially paired and partially unpaired data


Interpretation of log-transformed regression (Y = LN(Y)) when the independent variable (X) is a percentage


Probability that median falls between largest and smallest sample drawn

Probability that median falls within a range?


Statistically comparing 3 groups - Test for statistical difference

Comparing multiple mean scores using t-Test


PCA before and after standardization gives very different explained_variance_ratio_


AUC ROC Threshold Setting in heavy imbalance

Reduce Classification Probability Threshold


Distribution of the minimum of the components of a multivariate normal random variable

What is the probability that random variable $x_1$ is maximum of random vector $X=(x_i)$ from a multivariate normal distribution?


There are two variables. If they are not significant, can they be interaction items?

Including the interaction but not the main effects in a model


Is it possible to "sample size weight" the effects of multiple regressors to that of a "big" regressor?


Is it possible to refit after cross-validation and continue to train the model for better accuracy?

How to choose a predictive model after k-fold cross-validation?


Does the BatchNorm scale the distribution of whole layer (all neurons) or each neuron?

Dimensions of Scale (Gamma) and Offset (Beta) in Batch Norm


What does it mean if a regression model is not significant, but individual variables are?

How can you have a non-significant multiple regression model w/ significant predictors?


How does likelihood differ from probability?

What is the difference between "likelihood" and "probability"?


Can I use the Anova (type II) to test significance in my negative binomial regression?


Compute mean and variance of mixture of Gaussians given mean/variance of component gaussians

What is the variance of the weighted mixture of two gaussians?


How to best display the distribution of a large dataset with many outliers?

Boxplot equivalent for heavy-tailed distributions?


Test if two binomial distribution are significantly different from each other

Test if two binomial distributions are statistically different from each other


Definition of Likelihood in Bayesian Statistics

Is there any difference between Frequentist and Bayesian on the definition of Likelihood?


When is unbalanced data really a problem in Machine Learning?


Is it correct to write $\Bbb E[X]$ or $\Bbb E_{\theta}[X]$?


Expected of number of discrete uniform variables whose sum is bigger than k (from characteristic function of discrete Irwin–Hall distribution?)

Roll a 6-sided die until the total $\geq M$. Mean amount by which $M$ is exceeded?


Intuitive explanation for dividing by $n-1$ when calculating standard deviation?


How to measure smoothness/roughness of a time series

How to measure smoothness of a time series in R?


Is there ever a right time to not use Bessel's Correction?


Generalization of Bessel's correction to higher order models?

Why are the Degrees of Freedom for multiple regression n - k - 1? For linear regression, why is it n - 2?


Correct interpretation of coefficient estimates from GLM on binary outcome data

Interpreting a generalised linear mixed model with binomial data


Neural Network - Estimating Non-linear function

What should I do when my neural network doesn't learn?


Intuitions behind Singular Value Decomposing generalizing eigen decomposition

Relationship between SVD and PCA. How to use SVD to perform PCA?


Why the maximum sparsity is 99.5% in collaborative filtering?

Amount and sparsity of data for recommender systems


If a sample is normally distributed, does it mean a subsample is normally distributed, too?


Distribution of ratio of two independent normal variables

Simulating ratio of two independent normal variables


example of when the likelihood function does not sum up, or integrate to $1$?

What is the reason that a likelihood function is not a pdf?


removing outliers in skewed data for xgboost

why boosting method is sensitive to outliers


Validation of Models with Different Scale Data


Distribution of a ratio of uniforms: What is wrong?


Distribution of the square of a non-standard normal random variable


Why does Logistic Regression output show Z-test whereas Linear regression show T-test in the ouput?

Why use a z test rather than a t test with proportional data?


Difference between logistic regression and bayesian logistic regression?

Bayesian logit model - intuitive explanation?


Intuitively, why is the expectation of the score 0?

Why intuitively does $\mathbb E(\frac d {d\theta}\log p_\theta(x))=0$?


Tests of the effects of variables on imbalanced categorical variable

Does an unbalanced sample matter when doing logistic regression?


What can cause PCA to worsen results of a classifier?


Does it make sense to interact 2 dummy variables?


Data consisting of 110 samples and bach size of 10

Why do neural network researchers care about epochs?


What is the intuition behind the Metropolis-Hastings Algorithm?

How would you explain Markov Chain Monte Carlo (MCMC) to a layperson?


How to deal with perfect separation in logistic regression?


Identifying 1d clusters with scipy.stats or sklearn?

How do you find a cutting point / strong slope within one-dimensional data


Distribution where mean and mean of reciprocal are both 1

Constructing example showing $\mathbb{E}(X^{-1})=(\mathbb{E}(X))^{-1}$


Difference between W_T*X of Logistic regression and Linear regression

Why is logistic regression a linear classifier?


Density of square root of sum of squared independent uniform random variables

Expected minimum distance from a point with varying density


How do I apply PCA to a dataet containing continuous and categorical features?

Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables?


Does the feature selection matter for learning algorithm with regularization?

Do we still need to do feature selection while using Regularization algorithms?


What cross-validation to use on this data set, when selecting best model

How to evaluate/select cross validation method?


how to examine a relationship between categorical variables with several levels?

How to examine the relationship between categorical variables with several levels?


How can a sequence of random variables converges in probability to a constant?

Intuitive explanation of convergence in distribution and convergence in probability


Alternatives to one-way ANOVA for heteroskedastic data


How can I set the sample space for two random variables with 2 different discrete values for each?


Multi-dimensional CDF on a discrete support


If $c_i=a_ib_i, c_j=a_jb_j,$ $a_i$ and $a_j$ are independent, $b_i$ and $b_j$ are dependent, what about $c_i$ and $c_j$?

Functions of Independent Random Variables


Why do we need sigma-algebras to define probability spaces?


Doing principal component analysis or factor analysis on binary data


What is the mean of negative sign in PCA?

Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?


if 2 random variables have exactly same mean and variance


Deriving a constant in a probability mass function

Definition of Zero-truncated Poisson distribution


What are the differences between deep learning and neural networks?

difference between neural network and deep learning


X is a binomial random variable, then is aX+b follows a binomial distribution?

Linear transformation of a binomial random variable?


$T$ be minimal sufficient statistics. If $T = H(U)$ where $U$ has the same dimension as that of $T$, is $U$ minimal sufficient?

If the dimension of a sufficient statistic $T(X)$ equals the dimension of parameter space, $T(X)$ is minimal sufficient?


Pollinator abundance---sampled two years, fixed or random effect?


Working on Confidence Interval and its meaning

Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?


Does it make sense to up-sample imbalanced data if I care about predicting the right probabilities?

When is unbalanced data really a problem in Machine Learning?


What does p-value mean in Multiple Regression Analysis?

What is the meaning of p values and t values in statistical tests?


Multiple linear regression cannot be proceed

What is the effect of having correlated predictors in a multiple regression model?


How do I calculate the probability density function for a joint beta + uniform distribution?


Interpreting dummy variable odd ratio, 0.366 is more or less likely?

Help me understand adjusted odds ratio in logistic regression


2stage (instrumental variable) analysis: is reverse causality in the first stage a problem?

Does direction of causality between instrument and variable matter?


Online Algorithm Implementation for the Median

Algorithm to dynamically monitor quantiles


Probability of difference for uniform sample of consecutive numbers

Maximum gap between samples drawn without replacement from a discrete uniform distribution


What's the difference between error distribution and residual distribution in generalized linear models?

Question about the relationship between the variance of residuals and variances of the data points


Do generalized linear models allow non-normal response variables, non-normal errors, or both?

Logistic Regression - Error Term and its Distribution


Test fit of discrete data distribution to normal distribution


linear unbiased estimator alternative to OLS

Other unbiased estimators than the BLUE (OLS solution) for linear models


Clarification regarding confidence intervals

Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?


Will more training data of one class destroy the good model?

When is unbalanced data really a problem in Machine Learning?


PCA with continuous and categorical features

Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables?


Difference between F-test and T-test on OLS

Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?


What is the difference between Correlation and Regression for a layman ?

What's the difference between correlation and simple linear regression?


How are whiskers in a Boxplot of different lengths?


Is it possible to use ordinary least square (OLS) when the dependant variable is a “percentage” with a range from zero to hundred?

What are the issues with using percentage outcome in linear regression?


For univariate outlier analysis should I use z score if my data is skewed?

Outlier Detection on skewed Distributions


Dependent variable not correlated with independent, but still a predictor in regression

Can independent variables with low correlation with dependent variable be significant predictors?


If I do the same experiment many times then does a 95% credible interval mean 95% of the time the true value lies within that range?

Methods for testing a Bayesian method's software implementation


If X and Y both have the same pdf, they are identically distributed, but can I say that they are independent?

If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent?


Is there any test, like Mann Whitney U test or Kruskal Wallis test, that allows me to include a categorical covariate (like an ANCOVA)?

What is the non-parametric equivalent of a two-way ANOVA that can include interactions?


Calculate the standard error for a proportion of a group and a sub-group

Testing whether the mean of a group is different from the mean of the entire sample


how to handle multiple regression with indepndent variables are categorical as well as continous?

Dealing with Categorical variables in Multiple Regression


why is the variance of t-distribution with 1 and 2 degrees of freedom undefined while these distributions can be drawn?

Why does the Cauchy distribution have no mean?


Preprocess categorical variables with many values

Principled way of collapsing categorical variables with many levels?


Distribution of a logit transform of a normal variable


How can Poisson GLM work with non-count data (rate data)?

How is it possible that Poisson GLM accepts non-integer numbers?


logistic regression with an imbalanced data set, picking threshold cut point

How to choose the cutoff probability for a rare event Logistic Regression


Is it possible to gain point survival estimates from a coxme object?

How to generate predicted survivor curves from frailty models (using R coxph)?


Regression to the mean vs gambler's fallacy


Comparing the integral of a histogram and its distribution function


Choosing an ideal minibatch size for a large sample

What is the trade-off between batch size and number of iterations to train a neural network?


Predictor removed because of rank-deficiency in "lmer" model?

What is rank deficiency, and how to deal with it?


Statistical test for sample size equals one

What can we say about population mean from a sample size of 1?


Prior distribution for Bayesian binary logistic regression

Pick a prior for my bayesian generalised linear model with binary outcomes


Testing constraints/restrictions in multiple regression using R


How can I calculate $\int^{b}_{a}\Phi\left(\frac{x-\mu}{\sigma}\right)\phi(x)\,\mathrm dx$

What is $\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$ for $c\in\mathbb{R}$


Why are t-tests rather than z-tests used in linear regression?

Wald test in regression (OLS and GLMs): t- vs. z-distribution


Are Maximum Likelihood Estimators asymptotically unbiased?


Is feature selection with dummy coding of categorical variables problematic?

When LASSO selects only parts of a categorical variable?


Can I find MLE of probability of X greater than x

How to estimate $P(x\le0)$ from $n$ samples of $x$?


Perfect separation of a dummy variable with the dependent variable in a binary logistic regression produces high insignificant estimates

How to deal with perfect separation in logistic regression?


Linearity Assumption in Logistic Regression

Choosing between transformations in logistic regression


How to interpret the results from a binary model done in R?

Interpretation of R's output for binomial regression


Quantile of t distribution when the degree of freedom increases

Prove that $t_{n-1, \alpha/2}$ is strictly decreasing in $n$


Interpreting Odds Ratios For Logistic Regression

How to interpret regression coefficients in logistic regression?


Relation between Variance of one variable and variance of two independent variable

Variance of product of dependent variables


How should I interpret the coefficient in the output of this Logistic Regression?


How to compute effect sizes (cohen's d) for lmers in R?

How can I derive effect sizes in lme4 and describe the magnitude of fixed effects?


Why does centering/standardizing the regressor make the p value for the intercept zero?

Regression Proof that the point of averages (x,y) lies on the estimated regression line


Can somebody make it clear that when to use the average and when to use the mean?


Combining two means and SDs of one group


What do the joint distributions look like?

Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?


Is the canonical parameter (and therefore the canonical link function) for a Gamma not unique?


Factor Analysis on binary data (dimensionality check before IRT)

How do I appropriately examine the dimensionality of binary data?


Why is the square root of a number which is drawn from an exponetial distribution, Rayleigh distributed?


Why mean in Gaussian Process is not so important?

Why is the mean function in Gaussian Process uninteresting?


Why does gradient descent work faster with ReLU compared to using with Signoid?

How does rectilinear activation function solve the vanishing gradient problem in neural networks?


Is it okay to put augmented data in validation set?

How to do data augmentation and train-validate split?


How to compare two (linear) models with different predictors but the same predictor count?


Multivariable vs multivariate regression

Explain the difference between multiple regression and multivariate regression, with minimal use of symbols/math


Density Function of $T = (\bar{x})^2$ where $\bar{x}$ $\sim$ $N(\mu, 1/n)$

sum of noncentral Chi-square random variables


Non-technical reference for Bayesian probability

What is the best introductory Bayesian statistics textbook?


What statistical test do I use for differences in proportions?

Chi-square test or Z-test for comparing two proportions?


Mean and variance of a mixture distribution

What is the variance of the weighted mixture of two gaussians?


Difference between binary and count data of same data on logistic regression in R

Input format for response in binomial glm in R


validation accuracy is fluctuating in a neural network?

Learning a quadratic function using TensorFlow/Keras


How do you interpret the result of pca and biplot?


Calculating probabilities of completing a trading card/collector card set

How many stickers do I need to complete my FIFA Panini album?


Can a probability distribution value exceeding 1 be OK?


How to best characterize uncertainty for an incidence rate?

How to calculate 95% CI for cumulative incidence rate using R?


What does each graph cuadrant means with LDA vis plot from R?

What does each graph quadrant mean with LDAvis plot in R?


Crossed & nested random effects Mixed Effects


What should i do when my recurrent neural network doesn't improve?

What should I do when my neural network doesn't learn?


Interpretation of simple predictions to odds ratios in logistic regression


Tricky probability questions re Tenis match

If I have a 58% chance of winning a point, what's the chance of me winning a ping pong game to 21, win by 2?


Sum or average of gradients in (mini) batch gradient decent?

Mean or sum of gradients for weight updates in SGD


Equivalent of log sum exp trick for subtraction

Subtracting very small probabilities - How to compute?


ROC vs Precision-recall curves on imbalanced dataset


Do i need to use hyperparameters from gridSearch on whole training set to get final model?

How to obtain optimal hyperparameters after nested cross validation?


What is the relationship between the risk ratio and the weight of evidence?

Intuition behind Weight of Evidence and Information Value formula


Binary Logistic Regression Multicollinearity Tests


How can preprocessing with PCA but keeping the same dimensionality improve random forest results?

How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)?


Connection between t and F distributions

Linear Regression: P-values of t-test of significance of regression coeficients are same as p-values of F-test about submodel


StandardScaler to whole training dataset or to individual folds for Cross Validation

Combining PCA, feature scaling, and cross-validation without training-test data leakage


The product of 3 lognormals coming from tri-variate normal distribution

The product of two lognormal random variables


How to second-order timeseries data in deep learning?

Why does a time series have to be stationary?


Find correlation between binary variable and discrete variable

Is it meaningful to calculate Pearson or Spearman correlation between two Boolean vectors?


ANOVA, mixed model, or something else, for ordinal groups with a continuous outcome?

Likert item as independent variable for ANOVA?


What is E[X|Y>c] where Y=X+Z, and X, Z are normally distributed rvs?


How can i normalize the input data to neural network

How to encode categorical variables for neural networks


Measuring distribution/concentration across categories

How to express "inequality" of a distribution in one number?


Does random forest (and, decision tree) require an independent observation assumption?

On the importance of the i.i.d. assumption in statistical learning


Significant total and indirect effect but insignificant direct effect

Interpreting Mediation Output when Direct Effect is not Stat. Sig but ACME and Total are


What exactly is critical value in statistics? I confuse it with p-value and always get it wrong


What is the distribution when a Gaussian is passed through Sigmoid activation

Distribution of a logit transform of a normal variable


Linear Regression - with or without intercept

When is it ok to remove the intercept in a linear regression model?


Distribution of the top $m$ of $n$ samples of a Gaussian distribution?

Approximate order statistics for normal random variables


Asymptotic behaviour of logistic regression

Bias of maximum likelihood estimators for logistic regression


How to derive the formula for coefficient (slope) of a simple linear regression line?

Converting the beta coefficient from matrix to scalar notation in OLS regression


Solving Variance of Time Series AR process

The distribution of the initial point of an AR process


To find the covariance given the joint probability density function

Claims and questions regarding $n$-ball distribution?


Constructing a continuous distribution to match $m$ moments


My Neural Net can overfit but not generalize

What should I do when my neural network doesn't generalize well?


Is there any R package can smooth the coefficients as a function of coefficients sequence?

Forcing smoothness of regression coefficients


Strategy to deal with rare events logistic regression


How to check Logistic model assumptions in R?

Interpreting residual diagnostic plots for glm models?


Estimated standard deviation of difference between means in case of known and unknown variance?

From where term $\left(\frac{1}{n}+\frac{1}{m}\right)$ came in estimated variance of $\bar x - \bar y$


What is meant by "joint likelihood function" in this context?

Obtaining the likelihood of an individual observation


Correct formula for the std deviation of the difference between two means in case of unequal variance?


Metropolis Hastings algorithm and Markov chains

How would you explain Markov Chain Monte Carlo (MCMC) to a layperson?


How do get rid of (1 not defined because of singularities) in R?

Qualitative variable coding in regression leads to "singularities"


Best Time Series Analysis Book for Self Learning?

Books for self-studying time series analysis?


Why is accuracy not the best measure for assessing classification models?


Why does standardizing my data cause better results?

How and why do normalization and feature scaling work?


Ideas for outputting a prediction equation for Random Forests


Why a false positive is called type I error and a flase negative a type II error?


How to set up the matrix in data generation in R?


binomial GLM output hugely affected by a factor level with all zeros

How to deal with perfect separation in logistic regression?


Unpaired t-Test with equal sample sizes and unequal variances


How to prepare a 2x2 Confusion matrix for binary classifier, without code


Proposal distributions for covariance matrices in MCMC implementation of hierarchical models


Prove that the conditional distribution of a normal random variable is also normal random

What is the intuition behind conditional Gaussian distributions?


Confusion about Maximum likelihood estimation

Maximum likelihood function for mixed type distribution


Is the mean of n independent Bernoulli random variables normal?

What intuitive explanation is there for the central limit theorem?


How to calculate the minimum and maximum length of the 6th sample, using only measurement data of the first 5 samples?

Prediction intervals for a single random variable


Categorical ordinal data: which test is better?


Interpreting the coefficients when a ln10 transformed DV is predicted by a mixture of ln10 transformed, dummy (0 & 1 coded), and continuous IVs

Interpretation of log transformed predictor and/or response


how to interpret the result of significant regression of binary logistic yet all predictor is insignificant

How can a regression be significant yet all predictors be non-significant?


How to calculate Beta and coefficient of determination ($R^2$) from unstandardized coefficients in OLS regression?

Converting standardized betas back to original variables


Difference between offset and exposure in Poisson Regression


Is it possible to infer overfitting or underfitting from an accuracy vs epoch curve like the one below ? If yes, How?


How to prove three properties of the moment generating function?

Existence of the moment generating function and variance


Understanding Plurality Voting in Ensemble Methods

hard voting, soft voting in ensemble based methods


Is there a statement for the median like the central limit theorem for the mean?

Central limit theorem for sample medians


Zero-inflated Poisson regression Vuong test: Raw, AIC- or BIC-corrected results


How should I transform non-negative data including zeros?


Question about the meaning of Variance/Standard Deviation

Why square the difference instead of taking the absolute value in standard deviation?


How to interprete the following summerized data of a regression model?

What is a complete list of the usual assumptions for linear regression?


Which pseudo-$R^2$ measure is the one to report for logistic regression (Cox & Snell or Nagelkerke)?


I'm trying to analyze my data using mlogit. I get singularity issues. I am very new to statistical modelling. Help appreciated!

What is rank deficiency, and how to deal with it?


Binary Classification of Numeric Sequences with Keras and LSTMs

What should I do when my neural network doesn't learn?


Is there a single discrete distribution that handles over and under dispersion?

Is there a common underdispersed discrete distribution with unbounded support for general mean and variance?


R glmnet package: why is elasticnet parametrized like that?


White test for heteroscedasticity of simple linear regression in R

White's test for heteroskedasticity in R


Product of a linear function of IDD variables

Product of an exponential function of IDD variables


Mean and Variance of weighted sum of n random variables?

Variance of linear combinations of correlated random variables


How to define loss function for an unbalanced dataset?

Is there an optimal loss function for dealing with imbalanced classes?


Accuracy score or AUC extracted from Gradient Boosting Classifier of scikit-learn?

Compare classifiers based on AUROC or accuracy?


How to calculate error when $\sigma=0$ in a test sample?

How to tell the probability of failure if there were no failures?


Can one use ridge regression to test hypotheses?

Using regularization when doing statistical inference


What is the nonparametric variant of multivariate ANOVA with more than one one factor (and with interactions between factors)?

Is there a non-parametric equivalent of factorial MANOVA (at least 2x2)?


What is the best model for forecasting if you have very less data points?


Why is "stationarity" assumed in time series data?


How to input multiple categorical variables to Neural Network

How to build a predictive model when more levels of a categorical predictor are possible than appear in the training data


Logistic Regression with independently weighted regularization terms

R - Lasso Regression - different Lambda per regressor


Consider the sum of $n$ uniform distributions on $[0,1]$, or $Z_n$. Why does the cusp in the PDF of $Z_n$ disappear for $n \geq 3$?


Why cant Ridge Regression benift from negative lamda?


Regression betas of X on Y and Y on X are both less than one?

What is the difference between linear regression on y with x and x with y?


Poisson-Gamma conjunction - calculating posterior

Calculate posterior distribution (gamma-prior, poisson-likelihood)


A and B are have a significant correlation. B and C have a significant correlation. Can A and C still not correlate significantly?


Why Bootstrapping standard errors and 95% confidence intervals change each time I re-conducted the analysis

Bootstrapped confidence intervals: different values at every computation?


Stepwise feature selection for a classifier: use accuracy or loss?

Why is accuracy not the best measure for assessing classification models?


What is the connection between regularization and the method of lagrange multipliers ?


Name of mean absolute error analogue to Brier score?


How do we determine if the true population distribution has a finite mean and/or variance?


Does L1 regularization (Lasso) always leads to feature reduction?

Why does the Lasso provide Variable Selection?


Hurdle models in R: sign of the hurdle component coefficients

What is the difference between zero-inflated and hurdle models?


Why is it not possible to simplify $b=(X'X)^{-1}X'y$

Why the representation in the form of $Z'X(X'X)^{-1}X'Z$ can not be simplified into $Z'Z$


Controlling for baseline in pre-post between design: using $\Delta(T_2-T_1)$ or controlling for T1 in the regression model (or both)?

Best practice when analysing pre-post treatment-control designs


If $\beta$ can be expressed $\frac{\text{cov}(Y, \widetilde X) }{\text{var}(\widetilde X)}$... So where does the shared component of the variance go?

What happens to the shared explained variation in a regression? (Shown with Balentine graph)


Is 0 the unique center for the mixture density of $N(-a,\sigma^2)$ and $N(a,\sigma^2)$, each with weight 0.5?

Central Moments of Symmetric Distributions


Actions to take to improve validation accuracy

What should I do when my neural network doesn't generalize well?


Convergence in Distribution and Ordered Statistics

Convergence in Distribution in Order Statistics


What happens to Logistic Regression when the data is linearly separable?

How to deal with perfect separation in logistic regression?


What is the difference between correlation and mean absolute percentage error?


Transforming data with large negative and large positive values

Transforming positively skewed data with positive and negative values


Different results after updating the code (glmnet function)

Different seed gives different LASSO output


Fixing K-means that produces column clusters

Why does gap statistic for k-means suggest one cluster, even though there are obviously two of them?


The proof of shrinking coefficients using ridge regression through "spectral decomposition"


Calculate sample size for linear regression

Simulating data to fit a mediation model


What is the best way to visualize Likert-type dependent variables with 2x2 binary independent variables?

Graph for relationship between two ordinal variables


The inverse of the observed Fisher information matrix at the MLEs as an estimate of the var-cov matrix?

What kind of information is Fisher information?


Logistic Regression with dummy variables?

Confused about 0 intercept in logistic regression in R


Finding the Limiting Distribution of an order statistic

Consistency of an order statistic in exponential distribution


least square estimator of regression x onto y

What is the difference between linear regression on y with x and x with y?


Conditional Probability vs Dependent Events


is logistic regression only for binary classification?

Multinomial logistic regression analysis or binary logistic regression


How large should be a bootstrapping sample?

Resampling / simulation methods: monte carlo, bootstrapping, jackknifing, cross-validation, randomization tests, and permutation tests


What exactly is a Principal component and Empirical Orthogonal Function?

What exactly is called "principal component" in PCA?


How can I show that a Linear Regression line is increasing in time?

How to analyze trend in non-periodic time series


Choice of initial value for weights in Tensorflow MNIST Tutorial

Deep Neural Network weight initialization


Curse of dimensionality: is there a benchmark test set?

Generating a high-dimensional dataset where nearest neighbor becomes meaningless


Proportion of correct guesses knowing the true probabilities

To maximize the chance of correctly guessing the result of a coin flip, should I always choose the most probable outcome?


Can I usefully apply the Lyapunov CLT condition to a finite sum of Bernoulli random variables?

What is the CDF of the sum of weighted Bernoulli random variables?


How to do a bias-variance analysis on a machine learning modelling process


How could forcing my regression line to go through the origin increase the R^2?

Removal of statistically significant intercept term increases $R^2$ in linear model


What is the difference between a neural network and a deep neural network, and why do the deep ones work better?


Methods to quantify if the sum of two variables is close to a constant

Testing for linear dependence among the columns of a matrix


Which classification metric to use and why?

Which metric to use to evaluate highly imbalance classification model performance


Converting survey results from a 1-4 scale average to a 1-5 scale average

Convert a 1-9 scale average to a 1-5 scale average


Mapping R ARIMA parameters to coefficient symbols

Convert 'intercept/drift' term to 'constant' term in arima/auto.arima functions, in case of higher orders - R


Probits used in LD_50 is the same as the Wikipedia's probit definition?

How are the Error Function and Standard Normal distribution function related?


Normality assumption: how deal with them?

Is normality testing 'essentially useless'?


How to numerically find the mode of a joint probability distribution from samples?

Computationally efficient estimation of multivariate mode


Doubt in the sufficient statistic for the Location Family

Minimal Sufficient Statistic for location family


Why we cannot computing the integral of P(x) in Bayesian Inference analytically?

Why sometimes evidence is said to be too complex to compute and other times is negelected cause it is fixed?


Line of best fit does not look like a good fit. Why?

What does this plot tell me about my linear model?


what's the output of RNN (LSTM) in the prediction of time series


Find the probability that in a group of 23 people, exactly 3 people have birthdays on the same day

What is the real answer to the Birthday question?


Probability distribution of "large" number of independent events

Success of Bernoulli trials with different probabilities


How is the minimum of a set of IID random variables distributed?


What is the meaning of maximum likelihood estimation?

Maximum Likelihood Estimation (MLE) in layman terms


Doing principal component analysis or factor analysis on binary data


The reason why NMF has become so popular

What is the advantage of non-negativity in matrix factorization?


Is there an analog of Benjamini-Hochberg for Bayesian hypothesis testing?

Why don't Bayesian methods require multiple testing corrections?


Co-variance matrix, Eigen vector and Eigen values

Making sense of principal component analysis, eigenvectors & eigenvalues


Repeated training examples in Gradient Descent

Random initialization/order in neural network — bias or variance?


What are the 'critical' values of skewness and kurtosis for normality assumption?

Assumptions of linear models and what to do if the residuals are not normally distributed


BCa confidence interval and p-value disagreement. What coefficient to be reported?

Computing p-value using bootstrap with R


Question regarding "independent variables" term in regression analysis definition


How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?


If I want to estimate a population median from a bunch of sample medians, should I use their mean or their median?


GLM Binomial, with factor predictor, why model without the intercept

Confused about 0 intercept in logistic regression in R


For a posterior $p(\theta |y)$, if I specify a one-to-one transformation $\phi = g(\theta)$, how can I apply the transformation?

What is an example of a transformation on a posterior distribution such that the MAP estimate will be non-invariant?


How to easily determine the results distribution for multiple dice?


Distribution of the ratio of two i.i.d standard normals


Variable Selection using Principal Component Analysis

Using principal component analysis (PCA) for feature selection


Looking at the plot of two sample's distribution of means which are compared cannot reveal significance?

Relation between confidence interval and testing statistical hypothesis for t-test


Is it reasonable to get PC component score in the inverse direction to the original data?

Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?


Moving average process notation: negative or positive $\theta$s?


Autocorrelation of simple sine wave in R


Kullback-Leibler divergence: negative values?


What is the difference between a "link function" and a "canonical link function" for GLM


Covariance of binary and continuous variable


dropout: forward prop VS back prop in machine learning Neural Network


R - Data Simulation with Multiple Random Slopes


cosine of angle between random variables is equal to the correlation coefficient?

Building the connection between cosine similarity and correlation in R


We square at the variance and SD is it due a link with to Gaussian function?

Why are we using a biased and misleading standard deviation formula for $\sigma$ of a normal distribution?


How to check whether the missing data is MCAR, MAR, or MNAR?

How to decide whether missing values are MAR, MCAR, or MNAR


Good references for 'predictive models'?

Books for self-studying time series analysis?


Maximum likelihood of a neural network vs crossentropy loss

the relationship between maximizing the likelihood and minimizing the cross-entropy


Can a probability distribution value exceeding 1 be OK?


Equation (3.27) from Elements of statistical Learning

slope and intercept of linear regression


Adjusting the response variable to incorporate scaling effects

Predicting count data with random forest?


Are the two definitions of a sufficient statistic equivalent?

Is there a difference between Bayesian and Classical sufficiency?


What is bias in linear regression using NN

Understanding how many biases are there in a neural network?


What influences fluctuations in my Val accuracy figure?

What could be the reasons that making validation loss jumping up and down?


car::Anova with random factor or lmer with random factor

Difference between anova and Anova function


Can a non-conjugate prior lead to a closed form or analytically tractable posterior?


Large sample - statistical significance with minimal differences

Why is "statistically significant" not enough?


Is it necessary that an explicit feature map exists with all kernels?


How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models


Bayesian estimation difference between inferences is conjugate prior and non informative prior

Having a conjugate prior: Deep property or mathematical accident?


Assessing the Quality of a Normal Q-Q Plot


Why binary crossentropy can be used as the loss function in autoencoders?

Why is binary cross entropy (or log loss) used in autoencoders for non-binary data


Problems with central limit theorem and bigger SE with bigger samples


How does Ridge regression / Regularization help in selecting less or more important features?

Why does the Lasso provide Variable Selection?


What does it mean to transform a random variable into a different distribution?

Intuitive explanation for density of transformed variable?


Understanding the minimization of mean squared error function


What does vanishing gradient problem exactly mean?

How does LSTM prevent the vanishing gradient problem?


Should "kenward-roger"/"satterthwaite" degrees of freedom be used with "GLMM" fitted with penalized quasilikelihood"?

Is it beneficial/feasible to use kenward-roger/satterthwaite degrees of freedom in generalized estimating equations?


One sided test $H_0:\mu=0$ or $H_0:\mu\leq 0$?

Do null and alternative hypotheses have to be exhaustive or not?


biological basis for excluding values outside 3 standard deviations from the mean?

Detecting outliers using standard deviations


How to compute quantile of a mixed distribution?

How to find quantiles and likelihoods of mixture distributions?


Independence relation between observation and error

Independence and conditional distribution


Unable to interpret p statistics for periodicity testing of signals


Conflicting "facts" about the likelihood employed in Bayes theorem

Wikipedia entry on likelihood seems ambiguous


GLM distributions and link functions concept

Family of GLM represents the distribution of the response variable or residuals?


How do I show that the sample median minimizes the sum of absolute deviations?


Why do I have the same validation accuracy for every epoch?

What should I do when my neural network doesn't learn?


Violation of normality of residuals in glmm

Resolving heteroscedasticity in Poisson GLMM


Question on the choice of boundary in the CUSUM test when we make some resampling


Standard deviation of the sum of two normally distributed random variables with a weight


Which way is correct to write confidence intervals: [a; b] or (a; b)?

Are confidence intervals open or closed intervals?


Is there a Correlation metric for Categorical vs Numerical features?

Correlation coefficient between a (non-dichotomous) nominal variable and a numeric (interval) or an ordinal variable


Expected value for max weight of two stones (given independent uncertainty in each)

Expectation of max of two normal random variables


Determining true mean from noisy observations


What is the purpose of using a decision tree?


What are some introductions to classical statistics that emphasize unifying principles?

Books or resources for learning unified view of classical statistics?


Multiclass Segmentation Using U-Net: My training loss is not decreasing after certain epoch (accuracy not increasing)


SVD matrixes do not coincide with Eigen decomposition for covariance matrix

Weird correlations in the SVD results of random data; do they have a mathematical explanation or is it a LAPACK bug?


Setting boundaries for calculating $P(Y/X>2)$ choosing $dx/dy$ order


Need help understanding what a natural log transformation is actually doing and why specific transformations are required for linear regression

In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?


Dealing with Complete Separation in Logistic Regression when Reporting

How to deal with perfect separation in logistic regression?


What's the state of the art for time series forecasting in 2019?

State-of-the-art methods for forecasting time series array


How to calculate information included in R's confusion matrix


vector of three RVs that are pairwise Gaussian is Gaussian

Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?


In the classical setting of multiple linear regression, what is the multivariate distribution of beta hat?

Distribution of linear combination of OLS regression coefficients


Difference between deeper and wider neural networks

What is the difference between a neural network and a deep neural network, and why do the deep ones work better?


Get joint distribution from pairwise marginal distribution


What are the preconditions to fit a vector autoregression model?

VAR or VECM for a mix of stationary and nonstationary variables


How to measure correlation between categorical variable?

correlation between categorical variables


Why my covariate in a glm give me NA as a result?

Logistic regression in R returning NA values


Can the AUC (logistic regression) be used as a measure of quality of the model?

What is the difference in what AIC and c-statistic (AUC) actually measure for model fit?


Wilcox.test for testing count based data in R studio large W


How to do power analysis for Fisher exact test in tables larger than 2x2?

Computing the power of Fisher's exact test in R


Condition "Sample size > 30" for infering population proportion or mean

What references should be cited to support using 30 as a large enough sample size?


Checking the normality assumption for ANOVA test

ANOVA assumption normality/normal distribution of residuals


LC50 change in units and confidence limits


How can I find the marginal distributions of $\frac{X_1}{X_1+X_2}$ and $\frac{X_2}{X_1+X_2}$?

Construction of Dirichlet distribution with Gamma distribution


Why is the MLE for variance in single linear regression biased?

Why divide by $n-2$ for residual standard errors


Can a probability distribution value exceeding 1 be OK?


Ratio of two independent normal : cumulative sum

How can I obtain a Cauchy distribution from two standard normal distributions?


What are the conditions of applicability of linear regression?

What is a complete list of the usual assumptions for linear regression?


Sampling a proposed value with a limited range target when running MCMC

Metropolis Hastings proposal for one parameter restricted to less than the other


What to do with statistically insignificant dummy/categorical variables?

Can I ignore coefficients for non-significant levels of factors in a linear model?


How can a distribution have infinite mean and variance?


Finding the the Confidence Interval with Linear Extrapolation

Shape of confidence interval for predicted values in linear regression


Exponential distribution with mean 1/lambda

Finding $\mathrm{Var}(N)$ if $N=\inf\{n\ge1:\sum_{i=1}^nX_i>1\}$ where $X_i$'s are i.i.d Exponential variables


How do I write a logistic regression model?

How do I write a mixed-effect regression model (MRM)?


What, precisely, is a confidence interval?


Tensorflow - keras: bad performance for simple curve fitting task

What should I do when my neural network doesn't learn?


What does the y-axis of a normal distribution represent?

Can a probability distribution value exceeding 1 be OK?


Kernel:Why is the dot product a "measure of similarity" of instances?


Is there a point where you wouldn't use dummy variables? I.e., if getting dummy vars would lead to hundreds of variables?

Principled way of collapsing categorical variables with many levels?


What's the big deal with normalization constants in Bayesian inference?

Ignoring the normalising constant in Bayesian MCMC


Regression variables not used/applicable for certain cases

How do you deal with "nested" variables in a regression model?


In Simple Linear Regression $\hat \beta_1$ and $\bar Y$ are independent

Intuitive reason why jointly normal and uncorrelated imply independence


Correlation between Likert scale and four-categorical nominal scale

Correlation coefficient between a (non-dichotomous) nominal variable and a numeric (interval) or an ordinal variable


Interaction term and main effect multicollinearity

Collinearity diagnostics problematic only when the interaction term is included


Can someone give the intuition behind Mean Absolute Error and the Median?

Why does minimizing the MAE lead to forecasting the median and not the mean?


Can you explain Parzen window (kernel) density estimation in layman's terms?


Degrees of freedom in covariance calculation

Why shouldn't the denominator of the covariance estimator be n-2 rather than n-1?


How can RNN handle variable sized inputs?

How does an LSTM process sequences longer than its memory?


What is the meaning of p values and t values in statistical tests?


Adding a variable in multiple regression - interpretation?

How can adding a 2nd IV make the 1st IV significant?


Why is reparameterization trick necessary for variational autoencoders?

How does the reparameterization trick for VAEs work and why is it important?


understanding bias correction in ADAM algorithm

Understanding a derivation of bias correction for the Adam optimizer


Improving accuracy in time series forecasting

How to know that your machine learning problem is hopeless?


Why probabilities are measured over intervals (instead of points) for continuous probability distributions?

Why is the probability zero for any given value of a normal distribution?


What is the conceptual difference between posterior and likelihood?

Likelihood vs conditional distribution for Bayesian analysis


What are the assumptions for applying a quantile regression model?


Why do political polls have such large sample sizes?


Mahalanobis distance - understanding the formula

Bottom to top explanation of the Mahalanobis distance?


Intuitive reason why the Fisher Information of Binomial is inversely proportional to $p(1-p)$


How will random effects with only 1 observation affect a generalized linear mixed model?


Poisson regression with offset vs poisson regression with weight

Can Weights and Offset lead to similar results in poisson regression?


Rules of thumb for minimum sample size for multiple regression


What is the variance of the mixture distribution that is made up of 2 of the same distribution?

What is the variance of the weighted mixture of two gaussians?


testing significance among distributions

statistical significance among three distributions in R


How many ways are there of arranging the letters in the word

How to solve this combinatorial problem about selecting letters from different groups?


Loss reduction: when to use sum and when mean?

Mean or sum of gradients for weight updates in SGD


Why RMSE over MAE for matrix factorisation?

Mean absolute error OR root mean squared error?


How confident is my model? Is there a way to know?

Plotting confidence intervals for the predicted probabilities from a logistic regression


Variance of $k$th order statistic of normal vector


Testing if a regression coeffiecient is larger than another coeffeiceint

How we can compare two coefficients of one linear regression?


Logistic Regression Cost Function proof by using maximizing likelihood function

the relationship between maximizing the likelihood and minimizing the cross-entropy


Finding the MGF of a bivariate Normal Distribution

linear combination and univariate normal


What is the formal mathematical definition of a "layer" of a neural network?

What is the definition of layer in neural network?


Probability to guess the right coin without tossing


Absolute continuity of distributions --- why do we need this?

"Absolutely continuous random variable" vs. "Continuous random variable"?


Obtaining the $j$th component of the OLS - an explanation

Question on how to normalize regression coefficient


How to come up with this error estimation?

How do you get $\rm{var}(\Theta -\hat\theta) = \rm{var}(\Theta)$?


What does the 1/2 means in the L1 or L2 formula


Confusion about several different definitions of continuous random variables


Pearson VS Deviance Residuals in logistic regression


what is the simplified expression for the sum of probability of exponential distributed data?


What is the variance of the weighted mixture of two gaussians?


VECM Cointegration Relationship Coefficient(s) Interpretation

Error correction term has both positive and negative loadings - is that OK?


What is the meaning of p values and t values in statistical tests?


Can I use inferential statistics from a "non-random" sample of 34000?

Random Sample vs. As Large a Sample as Possible?


Calculating the confidence of probability estimates of binary outcome given small sample size?

Confidence interval for Bernoulli sampling


Probability density of conditional multivariate distribution

Deriving the joint probability density function from a given marginal density function and conditional density function


Why does the standard deviation sum squares of deviations from the mean instead of absolute deviations?

Why square the difference instead of taking the absolute value in standard deviation?


Calculating how much variability is due to different parameters

How to split r-squared between predictor variables in multiple regression?


R - is it ok to treat autocorrelation by randomly changing the order of variable

durbinWatsonTest() in R for non time-series data


Which Random Forest hyperparameters to tune with Grid Search and which are the best initial hyperparameters values?

What should be the optimal parameters for Random Forest classifier?


Obtaining eigenvectors of a matrix with more features than observations

Why are there only $n-1$ principal components for $n$ data if the number of dimensions is $\ge n$?


If higher order moment is finite, then lower order moment finite?

Prove that $E(X^n)^{1/n}$ is non-decreasing for non-negative random variables


automatic determination of the correct number of required clusters in text mining using R

How to decide on the correct number of clusters?


Probability mass function with variable probability?

Risk of extinction of Schrödinger's cats


What is the probability of a random variable larger than or equal to any other independent random variables?

What is the probability that random variable $x_1$ is maximum of random vector $X=(x_i)$ from a multivariate normal distribution?


How to calculate percentiles given standard deviation, mean and normality

What is inverse CDF Normal Distribution Formula


What is the expected value of $X$ given $X<Y$, where $X,Y\sim\mathcal{N}(\mu,\sigma^2)$?


GLMM using glmer() -- lack of convergence with a TEXTBOOK EXAMPLE


Can you use Cox Regression to model non-linear relationships?

Why is polynomial regression considered a special case of multiple linear regression?


How to use the Central Limit Theorem when you don't know the variance

Is there a theorem that says that $\sqrt{n}\frac{\bar{X} - \mu}{S}$ converges in distribution to a normal as $n$ goes to infinity?


What is Probabilistic Programming Used for?


I.i.d assumption to grant CLT on estimators of OLS

Functions of Independent Random Variables


What is the added benefit of conducting a "multivariate multiple regression" over several "multiple regressions"?

Multivariate linear regression vs. several univariate regression models


Which variable to take as reference category?


comparison of mean a subpopulation with entire population

Compare means of group with a mean of a subgroup


When is unbalanced data really a problem in Machine Learning?


Expectation of conditional uniform variates

Finding $E(X\mid X>Y)$ when $X,Y$ are i.i.d $U(0,1)$


is ANCOVA with a CATEGORICAL covariate legit? Two Way Anova a potential alternative?


Random Forest- change in model performance due to same values in one of the independent

independent variables in Random forest model


Running a Logistic regression - overflow error

Logistic regression model does not converge


Auto correlation function in R what are the error lines

Understanding the blue dotted lines in an ACF from R


Variable Importance in Multinomial Logistic Regression

Understanding which features were most important for logistic regression


Find $\mathbb{E} \bigg[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h}}{ \| \textbf{y} \|^{4} } \bigg]$ with Mathematica?

Direct way of calculating $\mathbb{E} \left[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h}}{ \| \textbf{y} \|^{4} } \right]$


Why the EM algorithm instead of a more direct computation?

Why should one use EM vs. say, Gradient Descent with MLE?


Confusion about random variables and what they mean


Bayesian modeling: likelihood function for continuous random variables, why is it not always 0?

Why does Maximum Likelihood estimation maximize probability density instead of probability


Does the magnitude of covariance have any real meaning?

How would you explain covariance to someone who understands only the mean?


Confidence intervals from bootMer in R, and pros/cons of different interval types

Prediction interval for lmer() mixed effects model in R


Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution?


Low loss and low accuracy. What is the reason?

Why does the accuracy not change, when applying different alpha values in L2 regularisation


Convolutional Neural Network - how to ensure filters of same layer learn different features?

Wouldn't multiple filters in a convolutional layer learn the same parameter during training?


Variable-length time series - neural network

Does the recurrent neural network require the length of input samples all the same


What should I do when my neural network doesn't learn?


Removing the dependency on training set size in L2 regularization in neural networks

Should we average weight decay loss in neural network?


Differences among dependence, statistical relationship and causation

What is the difference between correlation, causation and prediction?


Why autocorrelation of data lead to the lower estimation of standard error for coefficient?

Why autocorrelation affects OLS coefficient standard errors?


What algorithm is used in linear regression?


Distribution of X/(X+Y)of gamma variables

Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$


How can one express frequentist p-value in terms of Bayesian concepts?


How do you compute the slope for weighted least squares?

Formula for weighted simple linear regression


Calculating Confidence Intervals when proportion is skewed

Confidence interval around binomial estimate of 0 or 1


How to get an intuition to draw the eigenvectors for PCA?

Making sense of principal component analysis, eigenvectors & eigenvalues


Is there any statistical test to confirm if a dependent variable converges to a value as the independent variable approaches infinity?


How can I have a significant overall F-test but any significant P values for the individual coefficients? Graphical intuition, please?

Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?


Z = X1/(X1+X2) where X1 and X2 are gamma distributed

Construction of Dirichlet distribution with Gamma distribution


Positive correlation but negative beta coefficient


General Linear Model vs. Generalized Linear Model (with an identity link function?)


Are there some needs to prove that object function can be reduced to cost function?

Objective function, cost function, loss function: are they the same thing?


How can I interpret a model with good p-values and a bad R^2?

What does it mean if I have a high F-stat but low $R^2$?


What do we exactly mean by "density" in Probability Density function (PDF)?

Can a probability distribution value exceeding 1 be OK?


Computing a confidence interval for the difference between regression coefficients

Confidence interval around difference of regression coefficients


how to perform nested cross validation to the feature importance?


How do I prove that the expectation of sample variance is equal to the population variance for any distribution?

How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation?


How do you explain the condition under which a simple OLS regression model can be used to yield the causal effect of a treatment?

Under which assumptions a regression can be interpreted causally?


Why do the standardized residuals of a general linear mixed model using transformed data show a negative slope?

Unexpected residuals plot of mixed linear model using lmer (lme4 package) in R


What statistical test to use when both predictor and response are count data?

What statistical test to use for discrete predictor and response variables?


How to get R to deal with a 0 value in your dependent variable when you want to log your distribution


confidence intervals 95% we do z = qnorm( 0.95) or z = qnorm( 0.975)


Is there a problem with using logistic regression in a clinical trial with 2:1 randomisation?

Does an unbalanced sample matter when doing logistic regression?


Interpretation of level-log when the outcome is binary

interpreting level-log model that has a percentage variable


Why does LOOCV have a higher bias than a single validation set?

Bias and variance in leave-one-out vs K-fold cross validation


Log-Log regression not giving me elasticity


How can I find the mean and the standard deviation of X^2?

Expected value and standard deviation of $X^2$ in terms of moments of $X$


Justification of the log transformation of independent variables

In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?


Seasonality estimation without knowing the number of observations per seasonal cycle

Period detection of a generic time series


Interpretation of p values for each level of a covariate?

How to test the statistical significance for categorical variable in linear regression?


Transformation of Confidence Interval = Confidence Interval of Transformation?

Does invertible monotone transformation of a confidence interval give you a confidence interval (at the same level) in the transformed space?


General expression for a single coefficient $\hat{\beta_1}$ in a multiple linear regression?

Explicit solution for linear regression with two predictors


How to tune MCMC with unwieldy posterior

Converting (normalizing) very small likelihood values to probability


Does Frisch–Waugh–Lovell theorem change the covariance matrix on regression coefficients?


multiple regression coefficients - Standard error of intercept


Determining the roughness of a multidimensional optimization surface


Wikipedia entry on likelihood seems ambiguous


linear model without intercept : wrong r-square value?

Why I am getting different $R^2$ from R LM and manual calculation?


R choose which element of factor variable to throw out to produce only positive coefficients

How can factor-levels be automatically chosen in R to maximize the number of positive coefficients in a regression model?


Probability cut-off value for Logistic Regression


Is there a word for percentages, like "median" is for 50%?

"-iles" terminology for the top half a percent


Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?


Why is nls() giving me "singular gradient matrix at initial parameter estimates" errors?


Expectation and variance notation for ratio of random variables


Calculate expected cross entropy loss for a random prediction

Why does the first forward pass in a neural-network (NN) classification model computes to zero for all classes before final activation?


Will an OLS estimator for a regressor differ between a single linear regression and a multiple linear regression?

How exactly does one “control for other variables”?


Incremental updates for percentile estimates

Algorithm to dynamically monitor quantiles


transforming variables in a linear regression, do to all our just one?


What is the MLE of $\boldsymbol{\theta}=(\theta_1,\theta_2)$ for the random sample from $f(x|\boldsymbol{\theta})$?

MLE for 2 parameter exponential distribution


Calculating expected value of gamma-distributed random variable


Linear Mixed Model using R - what is the syntax when there are within-subject variables of both fixed and random nature?

Linear mixed model in R; modelling fixed effects with multiple levels and interactions. Help!


Can [single] Linear Regression be inferred from Multiple Regression?

What is the correct way to test for significant differences between coefficients?


Getting random number from Weighted sum of Normal distribution functions

Generating random variables from a mixture of Normal distributions


How to invert a mixture of log-logistic distributions?

How to find quantiles and likelihoods of mixture distributions?


Generating correlated samples from bernoulli variables

Generating correlated binomial random variables


How to handle categorical predictors with too many levels?

Principled way of collapsing categorical variables with many levels?


Why do we not get an R squared value for the intercept only term?

Removal of statistically significant intercept term increases $R^2$ in linear model


Finding variance-covariance of $\hat\beta$ from $\hat\beta = (X^TX)^{-1}X^Ty$

How to derive the covariance matrix of $\hat\beta$ in linear regression?


Uncertainty in Linear Regression Coefficients

Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom


Distribution of the squared length of a multivariate normal vector

Generalized Chi-Squared Distribution PDF


Reporting, figures: good practice to cut y-axes or not?

How to determine whether or not the y-axis of a graph should start at zero?


Is the definition of symmetric distribution using cdf correct?

What is the definition of a symmetric distribution?


Whitch tool is used to do such a quartile comparison

What's a good tool to create Sankey diagrams?


What is the difference between parametric and non-parametric distributions?


Distinction between "correlation matrix of the estimated parameters" and correlation matrix of original data columns?

What is the meaning of the correlation in glm


Purpose of the hidden variables in a Restricted Boltzmann Machine

What is the benefit of latent variables?


Is my model any good, based on the diagnostic metric ($R^2$/ AUC/ accuracy/ RMSE etc.) value?


Comprehensive list of activation functions in neural networks with pros/cons


how to interpret the contribution of a variable, when univariate vs multivariate analysis result differs (survival analysis)

Significant predictors become non-significant in multiple logistic regression


How to calculate joint distribution probability samples from the probabilities of the two univariate distributions?

Get joint distribution from pairwise marginal distribution


Why label encoding for categorical features should not be used for deep learning/neural network?

Why not approach classification through regression?


Dropout: scaling the activation versus inverting the dropout


Estimating the Parameters for $y=\beta_1 e^{\beta_2 x}+\beta_3 z+\epsilon$

Nonlinear regression model linear in some parameters


Interpretation of the Granger causality test

Interpreting Granger causality test's results


How to establish and prove causality between two variables?


Are feature selection methods prone to multicollinearity?

How to deal with multicollinearity when performing variable selection?


How to check whether or not two regression curves from different datasets are different in R

Compare the statistical significance of the difference between two polynomial regressions in R


How to tell if my mean values are not significantly different?

What is the meaning of p values and t values in statistical tests?


Why is entropy formula defined as what it is?

What is the role of the logarithm in Shannon's entropy?


How to ensure that a prediction will increase if a particular feature increases?

Constrain a Neural Network to be monotonic?


Time Dependent Coefficient in Cox Model using R

Textbook approach to modeling non-proportional hazards in the Cox model


how to interpret if the coefficients of two predictors are positive,the coefficient of the interaction term is negative?

Sign of Estimate (Coefficient) of Interaction Terms


What is the difference between logistic regression and neural networks?


Finding the optimal number of hidden nodes and training epochs for function approximation

Number of nodes in hidden layers of neural network


How is it possible to get a high $R^²$ & still have 'poor predictions'?

Is my model any good, based on the diagnostic metric ($R^2$/ AUC/ accuracy/ RMSE etc.) value?


How can I calculate $\int^{b}_{a}\Phi\left(\frac{x-\mu}{\sigma}\right)\phi(x)\,\mathrm dx$

How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$


why sum of squared errors for logistic regression not used and instead maximum likelihood estimation is used to fit the model?

What is happening here, when I use squared loss in logistic regression setting?


Correlation between continuous and binary variables

Correlations between continuous and categorical (nominal) variables


One component in PCA is always the mean vector in two-dimensions but not three

Does a correlation matrix of two variables always have the same eigenvectors?


Cross entropy versus Mean of Cross Entropy

Mean or sum of gradients for weight updates in SGD


What is the intuition behind the score function?

What kind of information is Fisher information?


Effect of class imbalance on logistic regression (mathematical basis)

Does an unbalanced sample matter when doing logistic regression?


Hint for problem including function of random variable?

What will be the variance of the following Random variable


Should we balance the data set if the data is intrinsically unbalanced?


What's the difference between regression and analysis of variance?


Reducing linear dependency among the columns of a matrix

Making sense of principal component analysis, eigenvectors & eigenvalues


What will be the value of AR and MA order?

Selecting ARIMA orders based on ACF-PACF vs. auto.arima


Determine useful predictors for logistic model

How to do logistic regression subset selection?


What is the intuitive explanation of Attention Maps?


What is the limit of the Box-Cox transformation as lambda goes to 0?


Classification of Bayesian probabilities

Classification of Bayesian posterior probabilities


Need some interpretation with plain English for a part in Bayesian Statistics with Beta proability distribution?

What is the intuition behind beta distribution?


understanding of method for confidence interval in regression

confidence intervals in linear regression


Can the 'bin size' in a histogram be thought of as a regularity constraint?


Under what conditions should I use an approximate Z-score vs a t-test?


Why is a prediction interval wider than a confidence interval for values of the predictor?

Difference between confidence intervals and prediction intervals


Intuitive explanation for inconsistency between regression and correlation coefficient sign


Why does the likelihood function of a binomial distribution not include the combinatorics term?

What does "likelihood is only defined up to a multiplicative constant of proportionality" mean in practice?


Finding joint distribution of sum of independent Poisson random variables and calculating probabilities

Deriving the bivariate Poisson distribution


Difference between Multivariate Regression vs Iterative Regression on Residuals

Question on how to normalize regression coefficient


How is this simplified pearson coefficient derived?

Relationship between $R^2$ and correlation coefficient


In what context are residuals from a plot important?

Why do we use residuals to test the assumptions on errors in regression?


Does the property of equivariance to translation of convolution layers help to learn translation-invariant features?

What is translation invariance in computer vision and convolutional neural network?


Is there any neural network whose output can be probabilistic, just like multi-class logistic regression?

Neural networks output probability estimates?


How can I compare two standard mortality ratios (SMRs)?

Poisson regression for modeling standardized mortality ratio (SMR)


Expectation maxmisation algorithm increases true likelihood at each iteration


On the importance of the i.i.d. assumption in statistical learning


How can I detect a line of points underneath lots of noise?


Confidence interval of the proportion in case of 0

Confidence interval around binomial estimate of 0 or 1


Do PCA affect different classification methods?


Question about using MCMC to estimate posterior probability from a random sequence?

Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution?


What is the differnce between simulation and estimation in bayesian statistics?


Random intercepts distribution looks normal but multimodal. Does this still follow the normality assumption?

Can you explain Parzen window (kernel) density estimation in layman's terms?


Expectation of any function of X, a nonnegative integer valued random variable

Expectation of a function of a random variable from CDF


sample space for a feature in machine learning


Interpretation of all negative values in PCA

Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?


Why we only use L1 and L2 in penalized regression

Why do we only see $L_1$ and $L_2$ regularization but not other norms?


Keras model with Google BERT -> very low accuracy

What should I do when my neural network doesn't learn?


When is unbalanced data really a problem in Machine Learning?


Proper Way to Combine Feature Selection and Hyperparameter Tuning?

How should Feature Selection and Hyperparameter optimization be ordered in the machine learning pipeline?


Sum of Exponential and Gamma Distributions

How do gamma distributions add and what would that model?


Doubling the tails in two-sample permutation test


How to tell the difference between linear and non-linear regression models?


Does the variable order matter in linear regression

What is the difference between linear regression on y with x and x with y?


I just installed the latest version of R. What packages should I obtain?

What R packages do you find most useful in your daily work?


What's wrong with my solution to canonical correlation analysis (CCA) using the SVD?

Canonical Correlation analysis without raw data (algebra of CCA)


What is the purpose of a neural network activation function?


How should I interpret these ACF / PACF plots for a time series?


Would you please give some examples on Bias-Variance Trade off?

Intuitive explanation of the bias-variance tradeoff?


Interpretation of linear, quadratic, cubic outputs of ordinal predictors in glm calculation

Selecting best model based on linear, quadratic and cubic fit of data


What are the differences between stochastic and fixed regressors in linear regression model?


Simulate correlation matrix using a given structure

How to simulate random correlation matrix containing off diagonal structures


Derive t-distribution PDF kernel from its definition

A normal divided by the $\sqrt{\chi^2(s)/s}$ gives you a t-distribution -- proof


What is a good algorithm for estimating the median of a huge read-once data set?

Algorithm to dynamically monitor quantiles


Is there a minimum number of entries in a bin to consider it for computing $\chi^2$ ? and for gaussian behaviour?

What to do when I have expected count <5 warning for a chi squared test?


Intrinsic topology and metrics... (looking for name of a method)

How to understand "nonlinear" as in "nonlinear dimensionality reduction"?


How many parameters are in a gated recurrent unit (GRU) recurrent neural network (RNN) layer?


Is it fine to use Chi-squared test with parameters estimated from the same dataset?


What statistical test should I use with count data?

Which test should I use for ordinal data?


How to sample from a joint probability distribution of two variables?

How to generate numbers based on an arbitrary discrete distribution?


Good books on autoregressive distributed lags (ARDL)

References on auto-regressive distributed lags (ARDL) model


Uses of MCMC samplers outside of Bayesian Inference?


Outlier detection in high dimensional data

What is the best way to identify outliers in multivariate data?


Are large $p$ and $q$ values for ARMA models bad?

Why does default auto.arima stop at (5,2,5)?


How do I complete the square with normal likelihood and normal prior?


Cluster kmeans comparison between two data sets

Mapping k-means cluster centers and origins (measuring k-means accuracy)


What do we exactly mean by a biased estimate?


Confidence interval for Bernoulli sampling


The Sums of squares in 3 way Anova in R output has changed as the order of the variables in the modes changes

The order of variables in ANOVA matters, doesn't it?


GEE, quasi-likelihood and what it generalizes


Comparing clustering stability over period of time

How to select a clustering method? How to validate a cluster solution (to warrant the method choice)?


What is the best references / books to get familiar with machine learning algorithms?

Good examples/books/resources to learn about applied machine learning (not just ML itself)


What is the meaning of p values and t values in statistical tests?


Why is ridge regression called "ridge", why is it needed, and what happens when $\lambda$ goes to infinity?


Distribution of sample standard deviation

Asymptotic distribution of sample variance of non-normal sample


What is the meaning of AUC being high when accuracy is not?

How is a ROCAUC=1.0 possible with imperfect accuracy?


How to interpret these acf and pacf plots


Chi-square test for more than 2x2 tables?

Chi-square test for more than 2 x 2 tables


Alternate (?) definition of sample variance

Intuitive explanation for dividing by $n-1$ when calculating standard deviation?


VAR or VECM for a mix of stationary and nonstationary variables


Coefficient of variation for nonparametric data

Is there a non-parametric Coefficient of Variation?


How does k-fold validation affect the model coefficients?

How to choose a predictive model after k-fold cross-validation?


How can i start learning about using neural networks for time series analysis and forecasting?

How to apply Neural Network to time series forecasting?


"Kernel density estimation" is a convolution of what?


TF-IDF vs just TF in text classification

Bag-of-Words for Text Classification: Why not just use word frequencies instead of TFIDF?


How to plot binary (presence/absence - 1/0) data against continuous variables

How to use boxplots to find the point where values are more likely to come from different conditions?


Reference or a mathematical equation for R squared and adjusted R squared for panel models used in the R package plm

Difference of $R^2$ between OLS with individual dummies to panel fixed effect model?


What is the difference between linear and non-linear time series?


Is there something wrong in my neural network model?

What should I do when my neural network doesn't learn?


What is exactly the non-normality requisite for nonparametric tests?

What if residuals are normally distributed, but y is not?


Non-parameteric test on 2*2 contingency table

Proper analyses for 2x2 contingency tables


GLM Logistic regression in R: one category is significant, but others are not. Should I drop the variable?

Can I ignore coefficients for non-significant levels of factors in a linear model?


Principle Component Analysis on categorical predictors

Doing principal component analysis or factor analysis on binary data


How to interpret multinomial regression results?

Interpreting exp(B) in multinomial logistic regression


Survival analysis without observing survival times

Statistical methods for data where only a minimum/maximum value is known


How to get Linear dependent columns indices in big dataset?

Testing for linear dependence among the columns of a matrix


Proof Verification: Joint variance of the product of a random matrix with a random vector


Calculation of population mean and standard deviation using a vector of sample means and standard deviations

How does one go about determining the standard deviation of an entire sample data set?


Intuition behind standard deviation greater than mean for all positive values

Standard deviation of revenue where numbers are only positive


Is it possible to find the combined standard deviation?


How to perform regression with different error variances?


Evaluate definite interval of normal distribution


Neural network to regress peaks in an image does not converge

What should I do when my neural network doesn't learn?


Statistics probability help - can someone confirm my solution?

Probability statistics - probability that 10 or more of the donors are Rh-negative?


How to determine the propensity score classifier validity?

Should I use a machine learning model to calculate propensity score?


Is binning of continuous data always bad for statistical tests?

What is the benefit of breaking up a continuous predictor variable?


What is acceptable in a prediction model accuracy?

Is my model any good, based on the diagnostic metric ($R^2$/ AUC/ accuracy/ RMSE etc.) value?


Why prefer poly() to I() ? Are they different?

How to include a linear and quadratic term when also including interaction with those variables?


Neural Networks input data normalization and centering

Data normalization and standardization in neural networks


Understanding stratified K fold cross validation results (for LSTM binary classification model)


(Binomal Distribution) With n = 20, p = 0.2, calculate the probability that 2X >4 (Homework)


intuition/logic behind comparing p-value and significance level

What is the meaning of p values and t values in statistical tests?


How much missing data can you replace with data imputation?

How much missing data is too much? Multiple Imputation (MICE) & R


Why is stationarity of an autoregressive process contigent upon location of the roots of the backshift polynomial?


What should I do when my neural network doesn't generalize well?


How do i compare ordinal score across two or more categories?

How do you estimate correlations between ordinal and binary data in SPSS?


Frisch-Waugh-Lovell Theorem: Partialing out a set of regressors

Question on how to normalize regression coefficient


How to calculate Area Under the Curve (AUC), or the c-statistic, by hand


What does multivariate regression get us that several univariate regressions do not?

When do we use a multivariate regression?


How to know that your machine learning problem is hopeless?


Is there a way to use the covariance matrix to find coefficients for multiple regression?


Does multivariate regression produce the same results as multiple, single regressions?

Why do we need multivariate regression (as opposed to a bunch of univariate regressions)?


Determining true mean from noisy observations


Not understanding factor in residual variance in linear regression

Finding the unbiased variance estimator in high dimensional spaces


Logistic regression always predicting 1 for my small data set

Logistic regression is predicting all 1, and no 0


Joint distribution of correlated poisson random variables

Deriving the bivariate Poisson distribution


T-test. Whether to assume equal or unequal variance

Always use Welch-t test (unequal variances t-test) instead of Student-t or Mann-Whitney test?


Different modes of stating probability law

Does product sigma algebra of n B(R) (borel) coincide with B(R^n)?


Should I adjust the number of epochs if it was determined using cross-validation?

Is epoch optimization in CV with constant mini-batch size even possible?


Equivalence between Mahalanobis distance and PCA (mathematical proof)

Bottom to top explanation of the Mahalanobis distance?


Why centering the data for machine-learning?

Is it a good practice to always scale/normalize data for machine learning?


Are features in Random Forest sampled with replacement

Random Forest mtry Spit-to-Split Variable Sampling Procedure


How to quantify the "resolution" of "Fractional factorial design"?

Intuition to the Resolution of a fractional factorial design


Comparing two groups with big gap in sample sizes?

Independent samples t-test with unequal sample sizes


How to combine categorical and numeric data in pytorch

What are appropriate methods for preparing categorical features for recurrent networks to ensure efficient backpropagation?


How are gradients defined for backprop in Torch autograd?

Step-by-step example of reverse-mode automatic differentiation


Is my NN underfitting? If yes how should I improve it?

What should I do when my neural network doesn't generalize well?


How to find the k value for K-Means clustering using scikit in python?

How to decide on the correct number of clusters?


What is the intuition behind beta distribution?


ANN resulted in less than 0.4 R-squared value. Is my methodology correct?


If $T(\bf{X})$ is a sufficient statistic for $\theta$, why does the conditional distribution of $\bf{X}$ given $T(\bf{X})$ doesn't depend on $\theta$?

Intutitive meaning behind the formal definition of sufficient statistic?


Intuitive understanding of the difference between consistent and asymptotically unbiased

What's the difference between asymptotic unbiasedness and consistency?


repeated measures ANOVA or one-way ANOVA for a radiology study?

Should I use repeated measures ANOVA or one-way ANOVA?


Optimal cut-off value for continuous covariate with binary outcome

What is the benefit of breaking up a continuous predictor variable?


VAR or VECM for a mix of stationary and nonstationary variables


Does it make sense to use logistic regression in R when both my IV and DV are dummies?

Logistic regression with binary dependent and independent variables


Expected value of X given Y is less than some constant


In bootstrapping, within a single instance of resampling, why do you draw a number of samples equal to your starting N?

Bootstrap sample with size greater than the original sample


Is my understanding of the relation between x on y and, y on x, simple linear regression as a vector transformation wrong?

What is the difference between linear regression on y with x and x with y?


Maximizing likelihood function of continuous normal distribution

In MLE for continuous rv, why is it ok to evaluate a pdf at a point?


What is the meaning of p values and t values in statistical tests?


Least square for binary classification {0, 1}: is the threshold always equal to 0.5?

Reduce Classification Probability Threshold


First difference in logs transformation produces biased results on back-transformation

Inverting logarithmic output from VAR model


How does the Rectified Linear Unit (ReLU) activation function produce non-linear interaction of its inputs?


How to get statistics of all samples through statistics of subsamples?


significance of pvalue for logistic regression

High p-values for logistic regression variable that perfectly separates?


What does it means getting p-values equal to 1 and complete separation in logistic regression?

How to deal with perfect separation in logistic regression?


Why is Poisson regression used for count data?


What is a Fully Bayesian Framework compared to MAP, MLE etc?

Relation Between Bayesian Estimation and Maximum a posteriori estimation


What about the covariance formula makes it obvious that it is about 'linear' associations?

Why does Covariance measure only Linear dependence?


Can we derive the Variance of the least squares slope WITHOUT assuming that $X_i$s are fixed or deterministic?


Why are random forest predictions over a smaller range than the true target variable?

Zero-inflated model predicting only a small range of values. I need help


What are kernels in support vector machine?

How to intuitively explain what a kernel is?


Why does feature scaling improves accuracy?

Is it a good practice to always scale/normalize data for machine learning?


In stepwise regression, how to interpret non-significant variables?

Algorithms for automatic model selection


Higher RMSE but lower MAE and RMLSE. Which model is better?

Mean absolute error OR root mean squared error?


Negative ICC value. Wrong test or wrong interpretation?


Why is factorial design advantageous to running single experiments?

Asking nature a single question or a carefully thought out questionnaire


Error with numeric class in GLM with Poisson distribution

Should I use an offset for my Poisson GLM?


Null deviance & Residual deviance meanings?

Interpreting Residual and Null Deviance in GLM R


When forcing intercept to zero, how R-squared is changed?

Removal of statistically significant intercept term increases $R^2$ in linear model


Why does the slope of the same coefficient change when we add new variables?


Making sense of principal component analysis, eigenvectors & eigenvalues


Is minimizing Koenker-Bassett error the only optimization problem that gives sample quantile?


OLS but accidentally swapping $X$ and $Y$ and calculating new parameters

Effect of switching response and explanatory variable in simple linear regression


Why is the p-value changing and what does it mean

Standardization of variables and collinearity


What' s $E[Y] = E[f(X)]$? $X\sim N(\mu,\sigma^2)$ and $f()$ is cdf of std normal rv?

How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$


Derivation of conditional expectation and variance of the AR(1) process

Conditional expectation in AR(1) process


How do I find the Logistic Distribution for a Logit Regression in R


Proportional allocation vs Neyman Allocation

Neyman allocation and proportional allocation


Is variable contribution to the top principal components a valid method to asses variable importance in a k-means clustering?

What is the relation between k-means clustering and PCA?


How is t-statistic calculated for coefficients in linear regression?

Standard errors for multiple regression coefficients?


Algebra of LDA. Fisher discrimination power of a variable and Linear Discriminant Analysis


Why is the quasi-Poisson in GLM not treated as a special case of negative binomial?


Recursive feature elimination and dropping dummy features

Recursive feature elimination and one-hot & dummy encoding?


Can one design neural networks to learn the ReLU activation function itself?


Can I combine ENTER method and Stepwise in a hierarchical regression?

What are the advantages of stepwise regression?


Sum of 3 correlated normal random variables

What is the distribution of the sum of non i.i.d. gaussian variates?


What is the test for association between 5 point likert scale and ordinal variable?

How to test for a monotonic relationship between two variables, without assuming a specific functional model?


How do you find the median of a long list of unsorted integers that can only be loaded in the memory in batches?

What is a good algorithm for estimating the median of a huge read-once data set?


How to derive this inverse standard deviation error bound for binomial random variable?

How to derive this MAE error bound on the central limit theorem?


Why does the Causal Impact Analysis uses Bayesian Structural Time Series Model?

Why isn't causal inference a simple specialized regression problem?


What are the best metrics to evaluate a multiclass classification model?

Why is accuracy not the best measure for assessing classification models?


Distribution of the dot product between random unit vectors

Distribution of scalar products of two random unit vectors in $D$ dimensions


Relationship between SVD and PCA. How to use SVD to perform PCA?


What is the variance of the weighted mixture of two gaussians?


Applying different kernels to parts of a dataset and merging the output

Proof of sum of kernels of concatenated vector


What justifies this calculation of the derivative of a matrix function?


Summary of All of Statistics in a useful mind map


Normally its easy to solving mean and covariance of Bernoulli Distribution but how we do when its Bernoulli Distribution vector in below Questions?


arima (0,1,0). How can I interpret it in this case?


What is an "uninformative prior"? Can we ever have one with truly no information?


Using BIC to estimate the number of k in KMEANS


Can someone please tell me what's the use of confusion matrix?


Can the t-test be used to test the difference between percentiles of 2 samples?

What statistical test allows comparison of the 3rd quartiles between groups?


Proof that the mean of predicted values in OLS regression is equal to the mean of original values?

Why do residuals in linear regression always sum to zero when an intercept is included?


Why is breaking symmetry important, when initializating the weights of a Neural Network?

Why doesn't backpropagation work when you initialize the weights the same value?


Are the confidence intervals and p-value for this risk consistent?


How to calculate quartiles and other percentiles?


How to calculate `mean` and `sd` of lognormal distribution based on `meanlog` and `sdlog`?

How to find normal and lognormal moments, given partial information?


Can this statistic be shown not to be sufficient for $\theta$?


Sample size calculation for mixed models


Deep learning model with both continuous and categorical features

How to recode categorical variable into numerical variable when using SVM or Neural Network


Optimal number of folds for nested cross-validation?

How to choose the right number of CV folds for the nested cross validation for a small sample?