applied bayesian methods - sta539

Course Objectives

  • Compute conditional probabilities using Bayes’ Theorem.
  • Compute conditional distributions using Bayes’ Theorem, demonstrate understanding of prior and posterior distributions, and compute conditional expectations using conditional distributions.
  • Apply methods for conjugate priors to perform Bayesian analyses for one proportion and for one mean. 
  • Fit a simple linear regression model using Bayesian methods.
  • Report and interpret credible intervals for estimating one proportion and one mean. 
  • Report and interpret Bayes’ factors for testing one proportion and one mean. 
  • Compute and interpret a predictive distribution, and use the predictive distribution to generate predictions. 
  • Utilize simulation-based methods such as Markov Chain Monte Carlo to estimate conditional distributions.
  • Apply Bayesian methods to a data analysis problem, and present the results in written and oral form.

Course Topics

Review of conditional probability and Bayes’ Theorem, conditional distributions and conditional expectations, and likelihood functions; Prior and posterior distributions; Conjugate priors; Credible intervals; Bayes’ factors; Bayesian estimation in linear models; Predictive analysis; Markov Chain Monte Carlo methods. Use of appropriate technology. Prerequisites: STA 506 and STA 511. 

Example Syllabus