Going off grid: computationally efficient inference for log-Gaussian Cox processes

• 成果类型: Article
• 署名作者: Simpson, D.; Illian, J. B.; Lindgren, F.; Sorbye, S. H.; Rue, H.
• 署名单位: University of Bath; University of St Andrews; University of Bath; UiT The Arctic University of Tromso; Norwegian University of Science & Technology (NTNU)
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv064
• 发表日期: 2016
• 页码: 4970
• 关键词: INVERSE PROBLEMS; approximation; models; distributions; diversity; patterns; FIELDS

摘要

This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making use of a continuously specified Gaussian random field. We show that for sufficiently smooth Gaussian random field prior distributions, the approximation can converge with arbitrarily high order, whereas an approximation based on a counting process on a partition of the domain achieves only first-order convergence. The results improve upon the general theory of convergence for stochastic partial differential equation models introduced by Lindgren et al. (2011). The new method is demonstrated on a standard point pattern dataset, and two interesting extensions to the classical log-Gaussian Cox process framework are discussed. The first extension considers variable sampling effort throughout the observation window and implements the method of Chakraborty et al. (2011). The second extension constructs a log-Gaussian Cox process on the world's oceans. The analysis is performed using integrated nested Laplace approximation for fast approximate inference.