Feasibility of Monte-Carlo maximum likelihood for fitting spatial log-Gaussian Cox processes

IF 2.1 2区 数学 Q3 GEOSCIENCES, MULTIDISCIPLINARY
Bethany J. Macdonald, Tilman M. Davies, Martin L. Hazelton
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引用次数: 0

Abstract

Log-Gaussian Cox processes (LGCPs) are a popular and flexible tool for modelling point pattern data. While maximum likelihood estimation of the parameters of such a model is attractive in principle, the likelihood function is not available in closed form. Various Monte Carlo approximations have been proposed, but these have seen very limited use in the literature and are often dismissed as impractical. This article provides a comprehensive study of the computational properties of Monte Carlo maximum likelihood estimation (MCMLE) for LGCPs. We compare various importance sampling algorithms for MCMLE, and also consider their performance against other methods of inference (such as minimum contrast) in numerical studies. We find that the best MCMLE algorithm is a practical proposition for parameter estimation given modern computing power, but the performance of this methodology is rather sensitive to the choice of reference parameters defining the importance sampling distribution.

蒙特卡罗极大似然拟合空间对数-高斯Cox过程的可行性
对数-高斯Cox过程(LGCPs)是一种流行且灵活的点模式数据建模工具。虽然这种模型参数的最大似然估计在原则上是有吸引力的,但似然函数不能以封闭形式提供。已经提出了各种蒙特卡罗近似,但这些在文献中使用非常有限,并且经常被视为不切实际而不予考虑。本文全面研究了lgcp的蒙特卡罗极大似然估计(MCMLE)的计算性质。我们比较了MCMLE的各种重要性采样算法,并在数值研究中考虑了它们与其他推理方法(如最小对比度)的性能。我们发现,在现代计算能力的条件下,最佳的MCMLE算法是一个实用的参数估计命题,但该方法的性能对定义重要抽样分布的参考参数的选择相当敏感。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Spatial Statistics
Spatial Statistics GEOSCIENCES, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
4.00
自引率
21.70%
发文量
89
审稿时长
55 days
期刊介绍: Spatial Statistics publishes articles on the theory and application of spatial and spatio-temporal statistics. It favours manuscripts that present theory generated by new applications, or in which new theory is applied to an important practical case. A purely theoretical study will only rarely be accepted. Pure case studies without methodological development are not acceptable for publication. Spatial statistics concerns the quantitative analysis of spatial and spatio-temporal data, including their statistical dependencies, accuracy and uncertainties. Methodology for spatial statistics is typically found in probability theory, stochastic modelling and mathematical statistics as well as in information science. Spatial statistics is used in mapping, assessing spatial data quality, sampling design optimisation, modelling of dependence structures, and drawing of valid inference from a limited set of spatio-temporal data.
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