Thermodynamic integration and steppingstone sampling methods for estimating Bayes factors: a tutorial. (English) Zbl 1431.62521
Summary: One of the more principled methods of performing model selection is via Bayes factors. However, calculating Bayes factors requires marginal likelihoods, which are integrals over the entire parameter space, making estimation of Bayes factors for models with more than a few parameters a significant computational challenge. Here, we provide a tutorial review of two Monte Carlo techniques rarely used in psychology that efficiently compute marginal likelihoods: thermodynamic integration [N. Friel and A. N. Pettitt, J. R. Stat. Soc., Ser. B, Stat. Methodol. 70, No. 3, 589–607 (2008; Zbl 05563360); N. Lartillot and H. Philippe, “Computing Bayes factors using thermodynamic integration”, Syst. Biol. 55, No. 2, 195–207 (2006; doi:10.1080/10635150500433722)] and steppingstone sampling [W. Xie et al., “Improving marginal likelihood estimation for Bayesian phylogenetic model selection”, Syst. Biol. 60, No. 2, 150–160 (2011; doi:10.1093/sysbio/syq085)]. The methods are general and can be easily implemented in existing MCMC code; we provide both the details for implementation and associated R code for the interested reader. While Bayesian toolkits implementing standard statistical analyses (e.g., JASP Team, 2017; R. D. Morey and J. N. Rouder, “BayesFactor: computation of Bayes factors for common designs” (2015; https://cran.r-project.org/package=BayesFactor)] often compute Bayes factors for the researcher, those using Bayesian approaches to evaluate cognitive models are usually left to compute Bayes factors for themselves. Here, we provide examples of the methods by computing marginal likelihoods for a moderately complex model of choice response time, the Linear Ballistic Accumulator model [S. D. Brown and A. Heathcote, “The simplest complete model of choice response time: linear ballistic accumulation ”, Cogn. Psychol. 57, No. 3 (2008; doi:10.1016/j.cogpsych.2007.12.002)], and compare them to findings of [N. J. Evans and S. D. Brown, “Bayes factors for the Linear Ballistic Accumulator Model of decision-making”, Behav. Res. Method 50, No. 2, 589–603 (2017; doi:10.3758/s13428-017-0887-5)], who used a brute force technique. We then present a derivation of TI and SS within a hierarchical framework, provide results of a model recovery case study using hierarchical models, and show an application to empirical data. A companion R package is available at the Open Science Framework: https://osf.io/jpnb4.
MSC:
| 62P15 | Applications of statistics to psychology |
| 62F15 | Bayesian inference |
| 65C05 | Monte Carlo methods |
Citations:
Zbl 05563360References:
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