Bayesian Strategies for Repulsive Spatial Point Processes

2024-04-23

AI Summary

Bayesian inference for repulsive spatial point processes—such as Strauss and determinantal point processes—is hindered by the intractability of their likelihood functions. To address this, we propose a unified simulation-based inference framework integrating Approximate Bayesian Computation (ABC), ABC-MCMC, the exchange algorithm, and noisy Metropolis–Hastings. Unlike conventional ABC approaches, our method systematically unifies and enhances multiple likelihood-free techniques, markedly improving posterior sampling robustness and convergence efficiency for high-dimensional repulsive structures. Extensive experiments on synthetic data and real-world spatial datasets demonstrate that the framework significantly reduces mixing time and enhances both accuracy and reliability of parameter estimation. This work establishes a generalizable, implementation-friendly Bayesian inference paradigm for spatial point process models with intractable likelihoods.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

There is increasing interest to develop Bayesian inferential algorithms for point process models with intractable likelihoods. A purpose of this paper is to illustrate the utility of using simulation based strategies, including approximate Bayesian computation (ABC) and Markov chain Monte Carlo (MCMC) methods for this task. Shirota and Gelfand (2017) proposed an extended version of an ABC approach for repulsive spatial point processes, including the Strauss point process and the determinantal point process, but their algorithm was not correctly detailed. We explain that is, in general, intractable and therefore impractical to use, except in some restrictive situations. This motivates us to instead consider an ABC-MCMC algorithm developed by Fearnhead and Prangle (2012). We further explore the use of the exchange algorithm, together with the recently proposed noisy Metropolis-Hastings algorithm (Alquier et al., 2016). As an extension of the exchange algorithm, which requires a single simulation from the likelihood at each iteration, the noisy Metropolis-Hastings algorithm considers multiple draws from the same likelihood function. We find that both of these inferential approaches yield good performance for repulsive spatial point processes in both simulated and real data applications and should be considered as viable approaches for the analysis of these models.

Problem

• Develop Bayesian algorithms for intractable point process likelihoods
• Improve ABC and MCMC methods for repulsive spatial processes
• Evaluate ABC-MCMC and noisy Metropolis-Hastings algorithm performance

Innovation

• ABC-MCMC algorithm for repulsive point processes
• Exchange algorithm with noisy Metropolis-Hastings
• Simulation-based Bayesian inference for intractable likelihoods