ABSTRACT
Bayesian inference has experienced a boost due to important advances in computational statistics. The likelihood of the model describes the data generating process given the parameters, and the prior usually reflects any knowledge about the model parameters. The posterior distribution is only available in closed form for a few models. Models with conjugate priors are those in which the prior is of the same form as the likelihood. For example, if the likelihood is a Gaussian distribution with known precision, the conjugate prior on the mean is a Gaussian distribution. In general, computational methods aim at estimating the integrals that appear in Bayesian inference. Markov chain Monte Carlo methods are a class of computational methods to draw samples from the joint posterior distribution. These methods are based on constructing a Markov Chain with stationary distribution the posterior distribution. The chapter also presents an overview of the key concepts discussed in this book.
