Fast, Approximate Maximum Likelihood Estimation of Log-Gaussian Cox Processes
提出一种结合变分近似和降秩插值的方法来拟合对数高斯Cox过程，利用自动微分和拉普拉斯近似实现高效优化，在模拟和实际数据中表现出更快的计算速度和良好的准确性。
Log-Gaussian Cox processes (LGCPs) offer a framework for regression-style modeling of point patterns that can accommodate spatial latent effects. These latent effects can be used to account for missing predictors or other sources of clustering that could not be explained by a Poisson process. Fitting LGCP models can be challenging because the marginal likelihood does not have a closed form and it involves a high dimensional integral to account for the latent Gaussian field. We propose a novel methodology for fitting LGCP models that addresses these challenges using a combination of variational approximation and reduced rank interpolation. Additionally, we implement automatic differentiation to obtain exact gradient information, for computationally efficient optimization and to consider integral approximation using the Laplace method. We demonstrate the method’s performance through both simulations and a real data application, with promising results in terms of computational speed and accuracy compared to that of existing approaches. Supplementary material for this article is available online.