Likelihood-Free Parameter Estimation with Neural Bayes Estimators

TL;DR

This paper introduces neural Bayes estimators for likelihood-free parameter estimation, demonstrating their speed, accuracy, and ease of use in complex models, with practical applications and open-source tools.

Contribution

It presents neural Bayes estimators as a fast, likelihood-free inference method, along with software tools and methods for handling replicated data using permutation-invariant networks.

Findings

Neural estimators efficiently estimate parameters in complex models.

They provide Bayes-optimal estimates with minimal computational effort.

Application to sea-surface temperature data shows rapid, reliable inference.

Abstract

Neural point estimators are neural networks that map data to parameter point estimates. They are fast, likelihood free and, due to their amortised nature, amenable to fast bootstrap-based uncertainty quantification. In this paper, we aim to increase the awareness of statisticians to this relatively new inferential tool, and to facilitate its adoption by providing user-friendly open-source software. We also give attention to the ubiquitous problem of making inference from replicated data, which we address in the neural setting using permutation-invariant neural networks. Through extensive simulation studies we show that these neural point estimators can quickly and optimally (in a Bayes sense) estimate parameters in weakly-identified and highly-parameterised models with relative ease. We demonstrate their applicability through an analysis of extreme sea-surface temperature in the Red Sea where, after training, we obtain parameter estimates and bootstrap-based confidence intervals from hundreds of spatial fields in a fraction of a second.