%0 Journal Article %1 gronau2017tutorial %A Gronau, Quentin F. %A Sarafoglou, Alexandra %A Matzke, Dora %A Ly, Alexander %A Boehm, Udo %A Marsman, Maarten %A Leslie, David S. %A Forster, Jonathan J. %A Wagenmakers, Eric-Jan %A Steingroever, Helen %D 2017 %K bayesian sampling %T A Tutorial on Bridge Sampling %U http://arxiv.org/abs/1703.05984 %X 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.

@article{gronau2017tutorial, abstract = {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.}, added-at = {2020-03-13T03:08:46.000+0100}, author = {Gronau, Quentin F. and Sarafoglou, Alexandra and Matzke, Dora and Ly, Alexander and Boehm, Udo and Marsman, Maarten and Leslie, David S. and Forster, Jonathan J. and Wagenmakers, Eric-Jan and Steingroever, Helen}, biburl = {https://www.bibsonomy.org/bibtex/26493e18c553516c165348842dd015b6f/kirk86}, description = {[1703.05984v2] A Tutorial on Bridge Sampling}, interhash = {ea7d986a1ca7c017910a40dbd6644f38}, intrahash = {6493e18c553516c165348842dd015b6f}, keywords = {bayesian sampling}, note = {cite arxiv:1703.05984}, timestamp = {2020-03-13T03:08:46.000+0100}, title = {A Tutorial on Bridge Sampling}, url = {http://arxiv.org/abs/1703.05984}, year = 2017 }