Year: 2025
Type: preprint
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 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 with implementation using the probabilistic programming language, Stan. 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 Bayesian inference. The method is then applied to the popular \textit{Beilschmiedia pendula Lauraceae} dataset.
Source: arXiv (Cornell University)
Authors: Collins, Kevin M., Schliep, Erin M.
Institution: North Carolina State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414878027
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