 # Introduction to Bayesian Statistics

Introduction to Bayesian Statistics
The scientific method; conditional probability; Bayes' Theorem; conjugate distributions: Beta-binomial, Poisson-gamma, normal-normal; Gibbs sampling.
STAT
251
 Hours 3.0 Credit, 3.0 Lecture, 0.0 Lab Prerequisites STAT 123 & STAT 240 & MATH 113 Taught Fall, Winter Programs Containing STAT 251
Course Outcomes:

### Bayes' Theorem

Explain how conditional probability and Bayes' Theorem relate to the analysis of data via the Bayesian paradigm

### Conjugate Priors, Binomial, and Poisson Distributions

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

### Gibbs and Metropolis Samplers

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

### Code in R

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

### Bayesian Analysis

Interpret and explain the results of Bayesian analysis