A brief introduction to the concepts and terminology behind Bayesian methods in preparation of our example lecture for using Bayesian regression for linear regression. We introduce the concepts of Bayes' theorem, the idea of MCMC and diagnostic plots/numerical summaries for the estimation, different quantities to estimate from the posterior distribution, and a comparison of using the brms package for different priors for a one-sample mean.
A video for the Advanced Biostatistical Methods I (BIOS 6618) course in the Department of Biostatistics and Informatics at the University of Colorado-Anschutz Medical Campus taught by Dr. Alex Kaizer. Slides and additional material available at https://www.alexkaizer.com/bios_6618.
00:00 Intro Song
00:21 Welcome
00:55 Frequentist versus Bayesian
02:04 Bayesian Overview (Bayes Theorem)
03:13 Likelihood
04:49 Prior
06:03 Normalizing Constant
06:50 Posterior
08:31 Bayes Theorem and Proportional To
10:33 MCMC Overview and Terminology
15:15 MCMC Diagnostics
15:45 Trace Plots
18:11 Autocorrelation Plots
19:20 Density/Histogram Plots
20:40 Numerical Diagnostics (Geweke, R-hat)
21:55 Bayesian Summaries from the Posterior
22:10 Point Estimate
23:47 Posterior Probability
25:17 Credible Intervals
27:36 Prior Specification Example (One-Sample Mean)
28:23 Priors to Compare
31:00 Plots of Likelihood, Prior, Posterior
35:07 Summary