用于协变量依赖点模式的贝叶斯软树泊松过程模型

中文摘要 AI 辅助

当积分强度函数无法解析计算时，从空间点模式估计协变量依赖的强度函数颇具挑战性；在贝叶斯推断中，由于需在高维协变量空间上反复积分强度函数，该挑战会进一步加剧。本文提出一种贝叶斯软树泊松过程模型，将自适应协变量划分与平滑强度函数相结合，核心思路是在树生成过程中采用软门控函数平滑划分边界间的过渡，同时保留积分强度的解析计算。该模型采用贝叶斯分类与回归树（Bayesian CART）先验从数据中学习划分结构，针对划分树，在叶节点参数上赋予共轭先验以实现解析边际似然计算；本文还开发了可逆跳跃马尔可夫链蒙特卡洛（RJ-MCMC）算法用于后验推断，证明了该模型关于赫尔利距离的后验一致性。大量模拟研究及野火数据应用均证实，所提方法优于现有方法。

英文摘要

Estimating covariate-dependent intensity functions from spatial point pattern is challenging when the integrated intensity function cannot be evaluated analytically. This challenge becomes even worse in Bayesian inference due to repeated integration of the intensity function over the high-dimensional covariate space. This paper develops a Bayesian soft-tree Poisson process model that combines adaptive covariate partitioning with smooth intensity function. The key idea is to use soft gating functions to smooth transitions between partition boundaries in a tree generating process while preserving analytic evaluation of integrated intensity. A Bayesian CART prior is adopted to learn the partition structure from data. Given the partition tree, conjugate priors are assigned on leaf parameters to enable analytic marginal likelihood computation. This paper also develops a reversible-jump Markov chain Monte Carlo (RJ-MCMC) algorithm for posterior inference. Posterior consistency is established for the proposed model with respect to the Hellinger distance. Extensive simulation studies and an application to wildfire data confirm the advantages of the proposed method over existing methods.

发表机构

• Iowa State University（爱荷华州立大学）

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