MCMC - Gibbs Sampling
30 Jul 2020 | Study NotesStudy Notes for Coursera Course: Bayesian Statistics: Techniques and Models by Matthew Heiner.
Compare to Metropolis Hasting (MH) that samples for a single parameter, Gibbs Sampling (GS) can sample for multiple parameters, and it does this one by one for each parameter. The important derivation to keep in mind is the following:
\[p(\theta, \phi|y) \propto g(\theta, \phi) \\ p(\theta, \phi|y) = p(\phi|y)p(\theta|\phi, y)\\ p(\theta|\phi, y)\propto p(\theta, \phi|y) \propto g(\theta, \phi) \\ p(\phi|\theta, y)\propto p(\theta, \phi|y) \propto g(\theta, \phi)\]Sampling for one parameter at a time when treating the other parameters as constants.
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