  The marginal likelihood plays an important role in many areas of Bayesian
statistics such as parameter estimation, model comparison, and model averaging.
In most applications, however, the marginal likelihood is not analytically
tractable and must be approximated using numerical methods. Here we provide a
tutorial on bridge sampling (Bennett, 1976; Meng & Wong, 1996), a reliable and
relatively straightforward sampling method that allows researchers to obtain
the marginal likelihood for models of varying complexity. First, we introduce
bridge sampling and three related sampling methods using the beta-binomial
model as a running example. We then apply bridge sampling to estimate the
marginal likelihood for the Expectancy Valence (EV) model---a popular model for
reinforcement learning. Our results indicate that bridge sampling provides
accurate estimates for both a single participant and a hierarchical version of
the EV model. We conclude that bridge sampling is an attractive method for
mathematical psychologists who typically aim to approximate the marginal
likelihood for a limited set of possibly high-dimensional models.
