Bayesian Inference: Optimal Decisions

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Page 3 of 4

Probability and Statistics: Independence and Conditional Probability

Explores independence and conditional probability in probability and statistics, with examples illustrating the concepts and practical applications.

Testing t-tests

Introduces t-tests, focusing on hypothesis testing and comparing coefficients using the t-distribution.

Hypothesis Testing: State of Nature

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

Introduction to Inference

Covers the basics of probability theory, random variables, joint probability, and inference.

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.

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 Significance: Maximum Likelihood Estimation and Confidence Intervals

Explores type I and type II errors, critical values, and confidence intervals in statistical significance.

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.

Describing Data: Statistics and Hypothesis Testing

Covers descriptive statistics, hypothesis testing, and correlation analysis with various probability distributions and robust statistics.

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.