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Thermodynamic integration via differential evolution: A method for estimating marginal likelihoods.

Nathan J Evans1, Jeffrey Annis2

  • 1Department of Psychology, University of Amsterdam, Amsterdam, Netherlands. nathan.j.evans@uon.edu.au.

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|January 4, 2019
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Summary
This summary is machine-generated.

We introduce thermodynamic integration via differential evolution (TIDE), a computationally efficient method for approximating marginal likelihoods in cognitive psychology. TIDE closely matches existing methods for non-hierarchical models and offers promising extensions for hierarchical models.

Keywords:
Bayes factorBayesian model selectionCognitive modelingMarginal likelihood

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Area of Science:

  • Cognitive Psychology
  • Computational Statistics
  • Bayesian Inference

Background:

  • Model selection in cognitive psychology relies on accurately estimating marginal likelihoods.
  • Calculating marginal likelihoods is often intractable, necessitating approximation methods like thermodynamic integration (TI).
  • Population Markov chain Monte Carlo (MCMC) methods, such as differential evolution MCMC (DE-MCMC), can be computationally expensive for TI.

Purpose of the Study:

  • To develop a computationally efficient method for approximating marginal likelihoods in cognitive models.
  • To reduce the computational burden of thermodynamic integration (TI) when using DE-MCMC.
  • To evaluate the performance of the proposed method for both non-hierarchical and hierarchical models.

Main Methods:

  • Proposed a novel method: thermodynamic integration via differential evolution (TIDE).
  • TIDE utilizes a single chain per power posterior, reducing computational cost compared to DE-MCMC.
  • Investigated TIDE's performance on non-hierarchical and hierarchical models, considering parameter sampling dependencies.

Main Results:

  • TIDE accurately approximates marginal likelihoods for non-hierarchical models, closely matching TI.
  • For hierarchical models, TIDE extensions showed good agreement with TI, though sampling assumptions had notable effects.
  • The proposed TIDE method offers a viable alternative for estimating marginal likelihoods.

Conclusions:

  • TIDE is a promising method for estimating marginal likelihoods in cognitive models, offering computational advantages.
  • Further research is needed for a comprehensive comparison of TIDE with other marginal likelihood estimation methods.
  • Understanding parameter sampling dependencies is crucial when applying TIDE to hierarchical models.