Bayesian Statistics: Hypothesis Testing and Estimation

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Bayesian Inference: Beta-Bernoulli Model

Explores the Beta distribution, Bayesian inference, and posterior calculation in the Beta-Bernoulli model.

Chi-Square Test: Independence Hypothesis

Explains the Chi-Square test for independence hypothesis and its practical applications.

Hypothesis Testing: Wilks' Theorem

Explores hypothesis testing using Wilks' Theorem, likelihood ratio statistics, p-values, interval estimation, and confidence regions.

Hypothesis Testing: State of Nature

Explores hypothesis testing, emphasizing the state of nature and the importance of choosing the most powerful test.

Likelihood Ratio Test: Hypothesis Testing

Covers the Likelihood Ratio Test and hypothesis testing methods using Maximum Likelihood Estimators.

Bayesian Inference: Gaussian Prior for Mean

Discusses Bayesian inference for the mean of a Gaussian distribution with known variance, covering posterior mean, variance, and MAP estimator.

Statistical Hypothesis Testing

Covers statistical hypothesis testing, likelihood estimation, and confidence intervals construction.

Likelihood Ratio Test: Hypothesis Testing

Explores hypothesis testing, emphasizing the likelihood ratio test and its applications in statistical analysis.

Exponential Family: Properties and Estimation

Explores exponential families, Bernoulli distributions, parameter estimation, and maximum entropy distributions in statistical modeling.

Statistical Theory: Inference and Optimality

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.