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A tutorial on bridge sampling

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A tutorial on bridge sampling. / Gronau, Quentin F.; Sarafoglou, Alexandra; Matzke, Dora et al.
In: Journal of Mathematical Psychology, Vol. 81, 12.2017, p. 80-97.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Gronau, QF, Sarafoglou, A, Matzke, D, Ly, A, Boehm, U, Marsman, M, Leslie, DS, Forster, JJ, Wagenmakers, E-J & Steingroever, H 2017, 'A tutorial on bridge sampling', Journal of Mathematical Psychology, vol. 81, pp. 80-97. https://doi.org/10.1016/j.jmp.2017.09.005

APA

Gronau, Q. F., Sarafoglou, A., Matzke, D., Ly, A., Boehm, U., Marsman, M., Leslie, D. S., Forster, J. J., Wagenmakers, E-J., & Steingroever, H. (2017). A tutorial on bridge sampling. Journal of Mathematical Psychology, 81, 80-97. https://doi.org/10.1016/j.jmp.2017.09.005

Vancouver

Gronau QF, Sarafoglou A, Matzke D, Ly A, Boehm U, Marsman M et al. A tutorial on bridge sampling. Journal of Mathematical Psychology. 2017 Dec;81:80-97. Epub 2017 Oct 23. doi: 10.1016/j.jmp.2017.09.005

Author

Gronau, Quentin F. ; Sarafoglou, Alexandra ; Matzke, Dora et al. / A tutorial on bridge sampling. In: Journal of Mathematical Psychology. 2017 ; Vol. 81. pp. 80-97.

Bibtex

@article{3a097696d0ed4926af9ab3aa6344d0e1,
title = "A tutorial on bridge sampling",
abstract = "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.",
keywords = "Hierarchical model, Normalizing constant, Marginal likelihood, Bayes factor, Predictive accuracy, Reinforcement learning",
author = "Gronau, {Quentin F.} and Alexandra Sarafoglou and Dora Matzke and Alexander Ly and Udo Boehm and Maarten Marsman and Leslie, {David S.} and Forster, {Jonathan J.} and Eric-Jan Wagenmakers and Helen Steingroever",
year = "2017",
month = dec,
doi = "10.1016/j.jmp.2017.09.005",
language = "English",
volume = "81",
pages = "80--97",
journal = "Journal of Mathematical Psychology",
issn = "0022-2496",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - A tutorial on bridge sampling

AU - Gronau, Quentin F.

AU - Sarafoglou, Alexandra

AU - Matzke, Dora

AU - Ly, Alexander

AU - Boehm, Udo

AU - Marsman, Maarten

AU - Leslie, David S.

AU - Forster, Jonathan J.

AU - Wagenmakers, Eric-Jan

AU - Steingroever, Helen

PY - 2017/12

Y1 - 2017/12

N2 - 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.

AB - 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.

KW - Hierarchical model

KW - Normalizing constant

KW - Marginal likelihood

KW - Bayes factor

KW - Predictive accuracy

KW - Reinforcement learning

U2 - 10.1016/j.jmp.2017.09.005

DO - 10.1016/j.jmp.2017.09.005

M3 - Journal article

VL - 81

SP - 80

EP - 97

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

SN - 0022-2496

ER -