The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data.
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机译：Log-Gaussian Cox Process是对空间点图案数据进行分析的常用模型。由于该模型具有双重随机性，因此很难拟合，即，它是第一级的泊松过程和第二级的高斯过程的分层组合。已经提出了各种方法来估计这种过程，包括传统的基于似然性的方法以及贝叶斯方法。在这里，我们重点讨论贝叶斯方法和在此框架内已考虑模型拟合的几种方法，包括哈密顿量蒙特卡洛（Hamiltonian Monte Carlo），集成嵌套拉普拉斯逼近和变分贝叶斯。我们考虑这些方法，并就统计和计算效率进行比较。这些比较是通过几个模拟研究以及两个应用程序进行的，第一个应用程序检查生态数据，第二个应用程序涉及神经影像数据。
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