Review of Hypothesis Testing framework (p-value, Type I/II errors). Statistical Power and Sample Size calculation. A/B Testing: Design, Execution, and Interpretation. Non-parametric Tests for non-normal data: Mann-Whi...
Review of Hypothesis Testing framework (p-value, Type I/II errors). Statistical Power and Sample Size calculation. A/B Testing: Design, Execution, and Interpretation. Non-parametric Tests for non-normal data: Mann-Whitney U test, Wilcoxon signed-rank test, Chi-Square tests for independence and goodness-of-fit.
Simple and Multiple Linear Regression. Coefficient estimation using Ordinary Least Squares (OLS). Model Evaluation: R-squared, Adjusted R-squared, Root Mean Squared Error (RMSE). Assumptions of Linear Regression and Diagnostic Procedures: Checking for Linearity, Independence (Durbin-Watson test), Normality of residuals (Q-Q plots), and Homoscedasticity (Breusch-Pagan test). Handling Multicollinearity with Variance Inflation Factor (VIF).
The Bayesian approach vs. the Frequentist approach. Components: Prior, Likelihood, Posterior, and Evidence. Conjugate Priors for simplifying posterior calculation. Bayesian Credible Intervals vs. Confidence Intervals. Introduction to computational methods for intractable posteriors: Markov Chain Monte Carlo (MCMC) and Gibbs Sampling.
The "Curse of Dimensionality." Principal Component Analysis (PCA): Mathematical foundation via Eigen-decomposition of the covariance matrix, Scree Plots for component selection, and interpretation of principal components. Linear Discriminant Analysis (LDA) as a supervised alternative for classification. Introduction to manifold learning with t-SNE for visualization.
Computationally intensive methods for inference and validation. Cross-Validation techniques (k-fold, Leave-One-Out) for robust model evaluation. Bootstrapping for estimating the uncertainty of statistics. Introduction to Generalized Linear Models (GLMs): Link functions, and the statistical foundation of Logistic Regression for binary classification.