A tutorial on bridge sampling. (English) Zbl 1402.62042

Summary: 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 [C.H. Bennett, “Efficient estimation of free energy differences from Monte Carlo data”, J. Comput. Phys. 22, 245–268 (1976; doi:10.1016/0021-9991(76)90078-4); X.-L. Meng and W. H. Wong, Stat. Sin. 6, No. 4, 831–860 (1996; Zbl 0857.62017)]), 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.


62F15 Bayesian inference
62P15 Applications of statistics to psychology


Zbl 0857.62017
Full Text: DOI arXiv


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