Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model

TL;DR

This paper introduces a scalable surrogate model for Bayesian inference of the inverse temperature in the Potts model, significantly improving computational efficiency for large spatial datasets like satellite imagery.

Contribution

We develop a parametric surrogate model that approximates the score function, enabling scalable Bayesian inference for the Potts model's inverse temperature parameter.

Findings

Achieves up to 100x faster inference than existing methods

Successfully applied to synthetic and satellite imagery data

Incorporates known properties of the likelihood such as heteroskedasticity

Abstract

The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a major influence over the resulting model fit. A difficulty arises from the dependence of an intractable normalising constant on the value of this parameter and thus there is no closed-form solution for sampling from the posterior distribution directly. There are a variety of computational approaches for sampling from the posterior without evaluating the normalising constant, including the exchange algorithm and approximate Bayesian computation (ABC). A serious drawback of these algorithms is that they do not scale well for models with a large state space, such as images with a million or more pixels. We introduce a parametric surrogate model, which approximates the score function using an integral curve. Our surrogate model incorporates known properties of the likelihood, such as heteroskedasticity and critical temperature. We demonstrate this method using synthetic data as well as remotely-sensed imagery from the Landsat-8 satellite. We achieve up to a hundredfold improvement in the elapsed runtime, compared to the exchange algorithm or ABC. An open source implementation of our algorithm is available in the R package "bayesImageS."