The Log-Gaussian Cox Process is a commonly used model for the analysis ofspatial point patterns. Fitting this model is difficult because of itsdoubly-stochastic property, i.e., it is an hierarchical combination of aPoisson process at the first level and a Gaussian Process at the second level.Different methods have been proposed to estimate such a process, includingtraditional likelihood-based approaches as well as Bayesian methods. We focushere on Bayesian methods and several approaches that have been considered formodel fitting within this framework, including Hamiltonian Monte Carlo, theIntegrated nested Laplace approximation, and Variational Bayes. We considerthese approaches and make comparisons with respect to statistical andcomputational efficiency. These comparisons are made through severalsimulations studies as well as through applications examining both ecologicaldata and neuroimaging data.
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机译：Log-Gaussian Cox Process是对空间点模式进行分析的常用模型。由于该模型具有双重随机性，因此难以拟合，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。已提出了多种方法来估计这种过程，包括基于传统似然的方法和贝叶斯方法。我们在此集中讨论贝叶斯方法以及在此框架内已考虑用于模型拟合的几种方法，包括哈密顿量蒙特卡洛（Hamiltonian Monte Carlo），积分嵌套拉普拉斯近似积分和变分贝叶斯。我们考虑这些方法，并就统计和计算效率进行比较。这些比较是通过一些模拟研究以及通过检查生态数据和神经影像数据的应用程序进行的。
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