Bayesian linear regression notes

Here is a great explanation of the Stein phenomenon. Here is a truly fantastic set of notes on Bayesian linear regression. Here is a short R script implementing a Gibbs sampler for the Bayesian linear regression model under the independent Normal-Gamma prior from section 1.4 of the above notes. Here is a picture of the Mogollon…

Hierarchical models

I'll have more to say here later, but for now here are the slides the R script the data

Gaussian mixture model

In class on Wednesday I briefly described a bivariate mixture model and I "live-coded" an R implementation of a Gibbs sampler for performing posterior inference. In this post I'm just going to revisit these same points. A Gaussian mixture model has a density function that is a weighted sum of Gaussian density functions, with weights…

Exercise solutions

In class recently we sketched out solutions to the first set of exercises. Below we write down those details so you can go over it more slowly at your convenience. As usual, pipe up if you see something incorrect. Let's first show that the mean is the optimal action under mean squared error. We start…

Bernoulli and Poisson models

Today in class we covered the Beta-Binomial model. That is, we considered a model where for $latex i = 1, \dots, n&s=1$, $latex Y_i \sim \mbox{Bernoulli}(\theta)&s=1$ independently and $latex \theta \sim \mbox{Beta}(a,b)&s=1$. For this model, the total number of successes, or $latex S = \sum_i Y_i&s=1$, is a sufficient statistic for the parameter $latex \theta&s=1$…

Bayesian preliminaries

David Blackwell interview. Demo script. Aside from some logistics and introductions, I had hoped to accomplish three things in the first class. Motivate the use of probability models for producing direct inferential statements. Point out points of departure from alternative approaches to statistics. Demonstrate the practical "work flow" of a simple Bayesian analysis. For the first objective,…

Spring 2018

This blog will serve as a platform for class notes from my two Spring 2018 graduate courses in Bayesian Statistics and Causal Inference at Arizona State University. I'm running the notes from WordPress because it has decent LaTeX support and it is easier than Blackboard. The first order of business is to test out the…