This class provides a practical introduction to Bayesian statistical inference, with an emphasis on applications in the social sciences. We will begin slowly, with a consideration of how Bayesian statistical inference differs from classical or frequentist inference. We will examine these differences in the context of simple statistical procedures and models: e.g., one and two-sample t-tests, the analysis of a two-by-two tables, one-way ANOVA, regression.

We then show how the explosion in desktop computing power since the 1990s has made Bayesian approaches attractive for more complex models. Specifically, the set of algorithms known as Markov chain Monte Carlo (MCMC) allows researchers to tackle classes of problems that used to fall in the ``too hard'' basket.

Today, MCMC is well and truly part of the statistical computing toolkit available to social scientists, and implemented in various forms in many different software packages (we will survey some of these, see below). We will examine how these algorithms make Bayesian inference feasible, their strengths and weaknesses, and some of the pitfalls to avoid when deploying MCMC algorithms.