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.
 Hours3.0 Credit, 3.0 Lecture, 0.0 Lab
 PrerequisitesMATH 112
 RecommendedConcurrent enrollment in MATH 113.
 TaughtFall, Winter
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