As its title suggests, this post is the third in a sequence of posts designed to introduce econometrics students to the use of Markov Chain Monte Carlo (MCMC, or MC2) methods for Bayesian inference. The first two posts can be found here and here, and I'll assume that you've read both of them already.
We're going to look at another example involving the use of the Gibbs sampler. Specifically, we're going to use it to extract the marginal posterior distributions from the joint posterior distribution, in a simple two-parameter problem. The problem - which we'll come to shortly - is one in which we actually know the answer in advance. That's to say, the marginalizing can be done analytically with some not-too-difficult integration. This means that we have a "bench mark" against which to judge the results generated by the Gibbs sampler.
Let's look at the inference problem we're going to solve.
Let's look at the inference problem we're going to solve.