Robustly estimating the marginal likelihood for cognitive models via importance sampling.

Area of Science:

• Bayesian inference
• Computational statistics
• Psychological modeling

Background:

• Markov chain Monte Carlo (MCMC) enables Bayesian inference for intractable likelihoods, but estimating marginal likelihood for model selection remains difficult.
• Current methods hinder testing psychological hypotheses using complex hierarchical models.
• Efficient marginal likelihood estimation is crucial for advancing Bayesian model selection.

Purpose of the Study:

• To propose an efficient method for estimating marginal likelihood in models with intractable likelihoods.
• To address limitations in Bayesian model selection for hierarchical psychological models.
• To provide a robust and computationally inexpensive approach for marginal likelihood estimation.

Main Methods:

• Utilizes Markov chain Monte Carlo (MCMC) to obtain model parameter samples.
• Employs an importance sampling (IS) framework with unbiased likelihood estimates.
• Constructs proposal densities using MCMC-generated samples for IS.

Main Results:

• The proposed method yields an unbiased estimate of the marginal likelihood.
• The estimator is robust to the quality of the sampling method used for proposals.
• Computationally efficient variance estimation for the marginal likelihood estimator is achieved.
• Convergence properties are established, with guidelines for optimizing computational efficiency.

Conclusions:

• The developed method offers an efficient and unbiased approach to marginal likelihood estimation for models with intractable likelihoods.
• This significantly improves Bayesian model selection capabilities, especially for hierarchical psychological models.
• The method is validated in complex scenarios, including choice modeling and cognitive model evaluation, with publicly available code.