# STAT 251

## Introduction to Bayesian Statistics

Statistics College of Physical and Mathematical Sciences

### Course Description

The scientific method; conditional probability; Bayes' Theorem; conjugate distributions: Beta-binomial, Poisson-gamma, normal-normal; Gibbs sampling.

Fall and Winter

3

3

3

0

Code in R

### Learning Outcome

Code in R a Gibbs sampler and/or Metropolis sampler for a simple non-conjugate posterior distributions

### Title

Bayesian Analysis

### Learning Outcome

Interpret and explain the results of Bayesian analysis

### Title

Conjugate Priors, Binomial, and Poisson Distributions

### Learning Outcome

Identify the conjugate priors of the normal (mean and variance), binomial, and Poisson distributions and derive the respective posterior distributions

### Title

Gibbs and Metropolis Samplers

### Learning Outcome

Explain why Gibbs and Metropolis samplers work and when they are appropriate to use

Bayes' Theorem

### Learning Outcome

Explain how conditional probability and Bayes&#39; Theorem relate to the analysis of data via the Bayesian paradigm