Fitting Log-Gaussian Cox Processes Using Generalized Additive Model Software

被引:2
作者
Dovers, Elliot [1 ,2 ]
Stoklosa, Jakub [1 ]
Warton, David I. [1 ]
机构
[1] UNSW Sydney, Sch Math & Stat, Sydney, NSW, Australia
[2] UNSW Sydney, Evolut & Ecol Res Ctr, Sydney, NSW, Australia
基金
澳大利亚研究理事会;
关键词
Basis functions; Generalized additive model; Point processes; Spatial statistics; POINT PROCESS MODELS; RANDOM-FIELDS; R PACKAGE; APPROXIMATION; PREDICTION; INFERENCE;
D O I
10.1080/00031305.2024.2316725
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
While log-Gaussian Cox process regression models are useful tools for modeling point patterns, they can be technically difficult to fit and require users to learn/adopt bespoke software. We show that, for suitably formatted data, we can actually fit these models using generalized additive model software, via a simple line of code, demonstrated on R by the popular mgcv package. We are able to do this because a common and computationally efficient way to fit a log-Gaussian Cox process model is to use a basis function expansion to approximate the Gaussian random field, as is provided by a generic bivariate smoother over geographic space. We further show that if basis functions are parameterized appropriately then we can estimate parameters in the spatial covariance function for the latent random field using a generalized additive model. We use simulation to show that this approach leads to model fits of comparable quality to state-of-the-art software, often more quickly. But we see the main advance from this work as lowering the technology barrier to spatial statistics for applied researchers, many of whom are already familiar with generalized additive model software.
引用
收藏
页码:418 / 425
页数:8
相关论文
共 44 条
[1]  
[Anonymous], 2017, GEN ADDITIVE MODELS, V2nd
[2]   inlabru: an R package for Bayesian spatial modelling from ecological survey data [J].
Bachl, Fabian E. ;
Lindgren, Finn ;
Borchers, David L. ;
Illian, Janine B. .
METHODS IN ECOLOGY AND EVOLUTION, 2019, 10 (06) :760-766
[3]   spatstat: An R package for analyzing spatial point patterns [J].
Baddeley, A ;
Turner, R .
JOURNAL OF STATISTICAL SOFTWARE, 2005, 12 (06) :1-42
[4]   Practical maximum pseudolikelihood for spatial point patterns [J].
Baddeley, A ;
Turner, R .
AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 2000, 42 (03) :283-315
[5]   Non-stationary Gaussian models with physical barriers [J].
Bakka, Haakon ;
Vanhatalo, Jarno ;
Illian, Janine B. ;
Simpson, Daniel ;
Rue, Havard .
SPATIAL STATISTICS, 2019, 29 :268-288
[6]   Stationary process approximation for the analysis of large spatial datasets [J].
Banerjee, Sudipto ;
Gelfand, Alan E. ;
Finley, Andrew O. ;
Sang, Huiyan .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2008, 70 :825-848
[7]  
BERMAN M, 1992, J ROY STAT SOC C, V41, P31
[8]   Quantifying the Effect of Geological Factors on Distribution of Earthquake Occurrences by Inhomogeneous Cox Processes [J].
Choiruddin, Achmad ;
Aisah ;
Trisnisa, Finola ;
Iriawan, Nur .
PURE AND APPLIED GEOPHYSICS, 2021, 178 (05) :1579-1592
[9]   Regularized estimation for highly multivariate log Gaussian Cox processes [J].
Choiruddin, Achmad ;
Cuevas-Pacheco, Francisco ;
Coeurjolly, Jean-Francois ;
Waagepetersen, Rasmus .
STATISTICS AND COMPUTING, 2020, 30 (03) :649-662
[10]   Fixed rank kriging for very large spatial data sets [J].
Cressie, Noel ;
Johannesson, Gardar .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2008, 70 :209-226