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