Lectures related to Foundations of statistics

Linear Algebra in Data Science

Explores the application of linear algebra in data science, covering variance reduction, model distribution theory, and maximum likelihood estimates.

Model Selection: AIC and BIC

Explores model selection using AIC and BIC criteria, addressing different questions and the importance of sparsity in selecting the best model.

Optimal Testing Methods

Explores optimal testing methods in statistics, focusing on the Neyman-Pearson framework and the construction of test functions for different types of hypotheses.

Maximum Likelihood Estimation: Theory and Examples

Covers maximum likelihood estimation, including the Rao-Blackwell Theorem proof and practical examples of deriving estimators.

Bayesian Statistics: Hypothesis Testing and Estimation

Covers hypothesis testing, p-values, significance levels, and Bayesian estimation.

Eliminating Nuisance Parameters: Statistical Inference

Covers the elimination of nuisance parameters in statistical inference using Lemmas 14 and 15.

Likelihood Ratio Tests: Optimality and Applications

Explores the theory and applications of likelihood ratio tests in statistical hypothesis testing.

Law of Large Numbers, Statistics

Covers the Law of Large Numbers in Statistics and methods for deriving estimators and maximum likelihood.

Statistical Tests: Wald and p-values

Explores statistical tests like the Wald test and p-values, emphasizing their calculation and interpretation.

Bayesian Inference: Precision in Gaussian Model

Explores Bayesian inference for precision in the Gaussian model with known mean, using a Gamma prior and discussing subjective vs objective priors.

Probability Models: Fundamentals

Introduces the basics of probability models, covering random variables, distributions, and statistical estimation.

Optimality in Decision Theory: Unbiased Estimation

Explores optimality in decision theory and unbiased estimation, emphasizing sufficiency, completeness, and lower bounds for risk.

Hypothesis Testing: Neyman-Pearson Framework

On hypothesis testing explores the Neyman-Pearson framework, test functions, errors, and likelihood ratio tests.

Statistical Estimation Methods

Covers statistical estimation methods, including maximum likelihood and Bayesian estimation.

Poisson Process: Density Theory and Applications

Explores Poisson processes, joint density, independence of events, and likelihood estimation.