Thermodynamic Integration and Steppingstone Sampling Methods for Estimating Bayes Factors: A Tutorial.

Area of Science:

• Computational statistics
• Cognitive modeling
• Bayesian inference

Background:

• Bayes factors are a principled approach for model selection.
• Estimating Bayes factors requires marginal likelihoods, posing computational challenges for complex models.
• Existing Bayesian toolkits often lack efficient methods for cognitive model evaluation.

Purpose of the Study:

• To review and demonstrate two efficient Monte Carlo methods for computing marginal likelihoods: thermodynamic integration (TI) and steppingstone sampling (SS).
• To provide practical implementation details and R code for applying TI and SS in cognitive modeling.
• To compare the performance of TI and SS against brute force methods for a response time model.

Main Methods:

• Tutorial review of thermodynamic integration (TI) and steppingstone sampling (SS).
• Implementation of TI and SS using Markov Chain Monte Carlo (MCMC) techniques.
• Application to the Linear Ballistic Accumulator (LBA) model of choice response time.

Main Results:

• TI and SS provide efficient computation of marginal likelihoods for complex Bayesian models.
• The methods were successfully applied to the LBA model, yielding comparable results to brute force techniques.
• Derivations and case studies demonstrate the utility of TI and SS within hierarchical modeling frameworks.

Conclusions:

• Thermodynamic integration and steppingstone sampling are valuable, efficient tools for estimating marginal likelihoods in cognitive modeling.
• These methods facilitate robust Bayesian model selection for researchers evaluating complex cognitive architectures.
• Accessible R code and tutorials empower researchers to implement these advanced computational techniques.