Black-box Bayesian inference for economic agent-based models

TL;DR

This paper tackles the problem of parameter estimation for complex economic agent-based models with intractable likelihoods. It advocates two black-box, neural approaches—neural posterior estimation (via normalising flows) and neural density ratio estimation—for efficient, discriminative inference on potentially high-dimensional, multivariate time-series data. Through tractable experiments and principled benchmarking against traditional KDE-based ABC methods, the authors show that these methods achieve state-of-the-art posterior recovery with orders-of-magnitude fewer simulations, while enabling rigorous validation via simulation-based calibration. The work also details round-based training, summary statistic learning, and practical benchmarking criteria that can guide future evaluation of approximate Bayesian inference methods in economics. Overall, the proposed methods have the potential to unlock scalable, uncertainty-aware Bayesian analysis for large-scale economic simulations.

Abstract

Simulation models, in particular agent-based models, are gaining popularity in economics. The considerable flexibility they offer, as well as their capacity to reproduce a variety of empirically observed behaviours of complex systems, give them broad appeal, and the increasing availability of cheap computing power has made their use feasible. Yet a widespread adoption in real-world modelling and decision-making scenarios has been hindered by the difficulty of performing parameter estimation for such models. In general, simulation models lack a tractable likelihood function, which precludes a straightforward application of standard statistical inference techniques. Several recent works have sought to address this problem through the application of likelihood-free inference techniques, in which parameter estimates are determined by performing some form of comparison between the observed data and simulation output. However, these approaches are (a) founded on restrictive assumptions, and/or (b) typically require many hundreds of thousands of simulations. These qualities make them unsuitable for large-scale simulations in economics and can cast doubt on the validity of these inference methods in such scenarios. In this paper, we investigate the efficacy of two classes of black-box approximate Bayesian inference methods that have recently drawn significant attention within the probabilistic machine learning community: neural posterior estimation and neural density ratio estimation. We present benchmarking experiments in which we demonstrate that neural network based black-box methods provide state of the art parameter inference for economic simulation models, and crucially are compatible with generic multivariate time-series data. In addition, we suggest appropriate assessment criteria for future benchmarking of approximate Bayesian inference procedures for economic simulation models.

Figures (6)

• Figure 1: Schematic of a normalising flow. Sampling and density evaluation are performed via the processes illustrated at the top and bottom of the figure, respectively.
• Figure 2: Visualisation: why standard Euclidean distances are misleading when gauging the performance of Bayesian inference algorithms. The parameter $\theta_2$ is ostensibly closer to the"true parameter" (grey) in this toy posterior than $\theta_1$. However, $\theta_1$ has higher posterior density, i.e. it is a more credible parameter given the observed data.
• Figure 3: (Brock & Hommes, parameter set 1) Posteriors obtained with each posterior estimation method. The marginal posterior distributions are located on the diagonals, while the bivariate joint distributions for each parameter pair are located on the upper diagonal. Red lines/dots indicate the mean of the true posterior.
• Figure 4: (Brock & Hommes, parameter set 2) Posteriors obtained with each posterior estimation method. The marginal posterior distributions are located on the diagonals, while the bivariate joint distributions for each parameter pair are located on the upper diagonal. Red lines/dots indicate the mean of the true posterior.
• Figure 5: (Multivariate geometric Brownian motion) Posteriors obtained with each estimation method. The marginal posterior distributions are located on the diagonals, while the bivariate joint distributions for each parameter pair are located on the upper diagonal. Red lines/dots indicate the mean of the true posterior.