Chapters 5, 13 and 14 presented methods for making inference about. infectious diseases from available data. This is of course one of the main motivations for modeling: learning about important features, such as R, the initial growth rate, potential outbreak sizes and what effect different control measures might have in the context of specific infections. The models considered in these chapters have all been simple enough to obtain more or less explicit estimates. of just a few relevant parameters. In more complicated and parameter-rich models, and/or when analyzing large data sets, it is usually impossible to estimate key model parameters explicitly. In such situations there are (at least) two ways to proceed. One uses Bayesian statistical inference by means of Markov chain Monte Carlo methods (MCMC), and the other uses large scale simulations along with numerical optimization to fit parameters to data. This chapter mainly describes Bayesian inference using MCMC and only briefly some large simulation methods.