标题： 基于Palm似然的空间点模式高效贝叶斯推断 显示英文标题

标题： Efficient Bayesian Inference for Spatial Point Patterns Using the Palm Likelihood

摘要： 贝叶斯推断用于空间点模式时，通常在计算上受到难以处理的似然函数的阻碍。 在频率学派文献中，利用伪似然函数的估计方程早已用于无需模拟的参数估计。 其中一种基于差分过程的伪似然被称为 Palm 似然。 利用贝叶斯复合似然和广义贝叶斯推断的概念，我们开发了一个框架，以便在贝叶斯背景下使用 Palm 似然。 Palm 似然的简单实现会导致模型参数后验覆盖不足。 我们提出了两种方法来解决这个问题并校准结果后验。 数值模拟展示了该方法在统计特性方面的有效性，以及与经典马尔可夫链蒙特卡罗相比在计算效率方面的优越性。 然后将该方法应用于流行的\textit{垂花木兰 木兰科}数据集。 显示英文摘要

摘要： 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.