Multi-objective Bayesian optimization for Likelihood-Free inference in sequential sampling models of decision making

TL;DR

This paper introduces MOBOLFI, a multi-objective Bayesian optimization method for likelihood-free inference that efficiently integrates multi-source data in sequential sampling models, improving parameter estimation and data source understanding.

Contribution

It extends LFI methods by modeling multi-source discrepancies with a multivariate approach, enabling better detection of conflicting information and more efficient inference in complex models.

Findings

MOBOLFI outperforms single-discrepancy methods in simulation efficiency.

It provides deeper insights into data source contributions.

Applied successfully to decision-making models with multi-source data.

Abstract

Statistical models are often defined by a generative process for simulating synthetic data, but this can lead to intractable likelihoods. Likelihood free inference (LFI) methods enable Bayesian inference to be performed in this case. Extending a popular approach to simulation-efficient LFI for single-source data, we propose Multi-objective Bayesian Optimization for Likelihood Free Inference (MOBOLFI) to perform LFI using multi-source data. MOBOLFI models a multi-dimensional discrepancy between observed and simulated data, using a separate discrepancy for each data source. The use of a multivariate discrepancy allows for approximations to individual data source likelihoods in addition to the joint likelihood, enabling detection of conflicting information and deeper understanding of the importance of different data sources in estimating individual parameters. The adaptive choice of simulation parameters using multi-objective Bayesian optimization ensures simulation efficient approximation of likelihood components for all data sources. We illustrate our approach in sequential sampling models (SSMs), which are widely used in psychology and consumer-behavior modeling. SSMs are often fitted using multi-source data, such as choice and response time. The advantages of our approach are illustrated in comparison with a single discrepancy for an SSM fitted to data assessing preferences of ride-hailing drivers in Singapore to rent electric vehicles.