Estimation and inference via Bayesian simulation: An introduction to Markov Chain Monte Carlo

Bayesian statistics have made great strides in recent years, developing a class of methods for estimation and inference via stochastic simulation known as Markov Chain Monte Carlo (MCMC) methods. MCMC constitutes a revolution in statistical practice with effects beginning to be felt in the social sciences; models long consigned to the too hard basket are now within reach of quantitative researchers. I review the statistical pedigree of MCMC and the underlying statistical concepts. I demonstrate some of the strengths and weaknesses of MCMC and offer practical suggestions for using MCMC in social-science settings. Simple, illustrative examples include a probit model of voter turnout and a linear regression for time-series data with autoregressive disturbances. I conclude with a more challenging application, a multinomial probit model, to showcase the power of MCMC methods.