Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoods

TL;DR

This paper introduces a neural network-based approach to approximate likelihood functions for spatial processes, enabling fast and accurate parameter estimation and uncertainty quantification even when likelihoods are computationally intensive or intractable.

Contribution

The authors develop a neural likelihood surface method using classification tasks and calibration, applicable to complex spatial processes with slow or intractable likelihoods.

Findings

Neural likelihood surfaces closely match exact or approximate likelihood estimates.

The method provides faster parameter estimation compared to traditional approaches.

Uncertainty quantification via calibrated neural likelihoods is reliable.

Abstract

In spatial statistics, fast and accurate parameter estimation, coupled with a reliable means of uncertainty quantification, can be challenging when fitting a spatial process to real-world data because the likelihood function might be slow to evaluate or wholly intractable. In this work, we propose using convolutional neural networks to learn the likelihood function of a spatial process. Through a specifically designed classification task, our neural network implicitly learns the likelihood function, even in situations where the exact likelihood is not explicitly available. Once trained on the classification task, our neural network is calibrated using Platt scaling which improves the accuracy of the neural likelihood surfaces. To demonstrate our approach, we compare neural likelihood surfaces and the resulting maximum likelihood estimates and approximate confidence regions with the equivalent for exact or approximate likelihood for two different spatial processes: a Gaussian process and a Brown-Resnick process which have computationally intensive and intractable likelihoods, respectively. We conclude that our method provides fast and accurate parameter estimation with a reliable method of uncertainty quantification in situations where standard methods are either undesirably slow or inaccurate. The method is applicable to any spatial process on a grid from which fast simulations are available.