R Package bayesImageS: Bayesian Methods for Image Segmentation using 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 R package provides implementations of Markov chain Monte Carlo algorithms for sampling from the intractable posterior distribution of the Potts model. The algorithms include pseudolikelihood, the exchange algorithm, path sampling, and approximate Bayesian computation. The following vignette explains these algorithms, providing the necessary theoretical background as well as implementation details specific to our R package. We address important questions such as how the computational cost increases with the size of the images, as well as how much accuracy is lost by using faster, more approximate methods. This document is intended to 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.