A Bayesian Joint Model for Multiple Point Processes with Application to Presence-Only Data

2026-07-02

AI Summary

This study addresses the challenge of effectively inferring presence-only data in joint modeling of multiple point processes, which is complicated by preferential sampling and partial observability. The authors propose a Bayesian joint modeling framework that, for the first time, incorporates Bayesian networks into multi-point process modeling to explicitly represent inter-process dependency structures. By introducing latent variables, the framework renders the likelihood tractable, enabling direct inference of both the number and spatial distribution of unobserved events. Combining hierarchical Bayesian modeling with MCMC and block Gibbs sampling, the approach facilitates simultaneous inference of inter-process relationship strengths and environmental covariate effects. Simulations accurately recover true parameters, and applications to Amazonian archaeological sites and tree species presence data corroborate existing literature by revealing a significant influence of pre-Columbian human activity on the distribution of specific tree species.

Abstract

Joint modeling of multiple point processes is relevant in applications where relationships among processes are of interest, such as in ecological and archaeological studies. Statistical inference becomes particularly challenging when multiple processes are analyzed jointly and the observed data correspond to presence-only patterns, which are subject to preferential sampling and partial observability. This paper proposes a Bayesian joint model for multiple point processes, with application to the presence-only setting. The dependence between processes is explicitly incorporated into the probabilistic specification of the model using Bayesian networks. Direct use of the likelihood leads to intractable likelihood functions. Latent data processes are then introduced so that the augmented likelihood function becomes tractable and can be exactly evaluated. This formulation also enables direct inference on the number and the spatial distribution of unobserved occurrences of any of the point patterns. Inference is carried out using Markov chain Monte Carlo with blocked Gibbs sampling. Simulation studies demonstrate that the proposed inferential scheme is able to recover the true model parameters. The proposed model is applied to real presence-only data of archaeological sites and tree species from Amazonia, as part of the study of the effect that pre-Columbian Indigenous presence might have on the occurrences of relevant tree species. The results are consistent with the findings reported in the literature. They also illustrate how the proposed model enables inference on the existence and on the magnitude of the relation between processes, in addition to their association with environmental covariates.

Problem

• multiple point processes
• presence-only data
• preferential sampling
• partial observability
• joint modeling

Innovation

• Bayesian joint model
• multiple point processes
• presence-only data
• latent data augmentation
• Bayesian networks