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arXiv · 2208.12942

Likelihood-Free Parameter Estimation with Neural Bayes Estimators

Matthew Sainsbury-Dale·Andrew Zammit-Mangion·Raphaël Huser
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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.

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Matthew Sainsbury-Dale, Andrew Zammit-Mangion, Raphaël Huser. 2022-08-27. Likelihood-Free Parameter Estimation with Neural Bayes Estimators. https://doi.org/10.1080/00031305.2023.2249522

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