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Bayesian Linear Regression

While much of our semester has focused on frequentist methods, we can also implement regression models in the Bayesian framework. In this lecture we revisit our multiple linear regression model lecture's data set and MLR to refit it from a Bayesian perspective. We explore 3 different prior specifications ("noninformative", "informative", and poorly specified) to see how the posterior does (or does not) differ. All examples are coded in R using the brms package. 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 00:22 Welcome 00:53 Motivating Dataset and Frequentist MLR 03:07 Bayesian Priors Considered 05:01 Non-Informative Prior MLR 07:01 Summary of brms Model 11:50 Density and Trace Plots 13:27 Autocorrelation Plots 14:01 HPD Intervals 15:11 Extracting Posterior Chains 16:35 Calculating Posterior Probabilities 18:12 Posterior Probabilities for Predicted Y 19:31 Mean/Median Posterior Estimates 20:09 Informative Prior Example 21:33 Nonsensical Prior Example 23:20 Summary