Efficient Bayesian Inference for Spatial Point Patterns Using the Palm Likelihood

Abstract: Bayesian inference for spatial point patterns is often hindered computationally by intractable likelihoods. In the frequentist literature, estimating equations utilizing pseudolikelihoods have long been used for simulation-free parameter estimation. One such pseudolikelihood based on the process of differences is known as the Palm likelihood. Utilizing notions of Bayesian composite likelihoods and generalized Bayesian inference, we develop a framework for the use of Palm likelihoods in a Bayesian context. Naive implementation of the Palm likelihood results in posterior undercoverage of model parameters. We propose two approaches to remedy this issue and calibrate the resulting posterior. Numerical simulations illustrate both the efficacy of the method in terms of statistical properties and the superiority in terms of computational efficiency when compared to classical Markov chain Monte Carlo. The method is then applied to the popular \textit{Beilschmiedia pendula Lauraceae} dataset.