08-MCMC-00-intro.Rmd

# Stochastic Explorations Using MCMC

In this chapter, we will discuss stochastic explorations of the model space using Markov Chain Monte Carlo method. This is particularly usefull when the number of models in the model space is relatively large. We will introduce the idea and the algorithm that we apply on the kid's cognitive score example. Then We will introduce some alternative priors for the coefficients other than the reference priors that we have been focused on. We will demonstrate using Markov Chain Monte Carlo on the crime data set to see how to use this stochastic method to explore the model space and how different priors may lead to different posterior inclusion probability of coefficients. Finally, we will summarize decision making strategies under Bayesian model uncertainty.