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

The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a substantial 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. These algorithms differ in their levels of accuracy and their scalability for datasets of realistic size. This study compares pseudolikelihood, the exchange algorithm, path sampling, and approximate Bayesian computation. We assess their accuracy and scalability using synthetic data as well as 2D remote sensing and 3D medical images. Our findings provide guidance on selecting a suitable algorithm for Bayesian image analysis. For nontrivial images, this necessarily involves some degree of approximation to produce an acceptable compromise between accuracy and computational cost.