Statistical Analysis of Spatial and Spatio-Temporal Point Patterns

TLDR: In this paper, the second-order intensity of spatial point patterns is estimated using the K-function and goodness-of-fit assessment using nearest neighbor distributions, which is based on the past Empirical and mechanistic models.

Abstract: Introduction Spatial point patterns Sampling Edge-effects Complete spatial randomness Objectives of statistical analysis The Dirichlet tessellation Monte Carlo tests Software Preliminary Testing Tests of complete spatial randomness Inter-event distances Nearest neighbor distances Point to nearest event distances Quadrat counts Scales of pattern Recommendations Methods for Sparsely Sampled Patterns General remarks Quadrat counts Distance measurements Tests of independence Recommendations Spatial Point Processes Processes and summary descriptions Second-order properties Higher order moments and nearest neighbor distributions The homogeneous Poisson process Independence and random labeling Estimation of second-order properties Displaced amacrine cells in the retina of a rabbit Estimation of nearest neighbor distributions Concluding remarks Nonparametric Methods Estimating weighted integrals of the second-order intensity Nonparametric estimation of a spatially varying intensity Analyzing replicated spatial point patterns Parametric or nonparametric methods? Models Contagious distributions Poisson cluster processes Inhomogeneous Poisson processes Cox processes Trans-Gaussian Cox processes Simple inhibition processes Markov point processes Other constructions Multivariate models Model-Fitting Using Summary Descriptions Parameter estimation using the K-function Goodness-of-fit assessment using nearest neighbor distributions Examples Parameter estimation via goodness-of-fit testing Model-Fitting Using Likelihood-Based Methods Likelihood inference for inhomogeneous Poisson processes Likelihood inference for Markov point processes Likelihood inference for Cox processes Additional reading Point Process Methods in Spatial Epidemiology Spatial clustering Spatial variation in risk Point source models Stratification and matching Disentangling heterogeneity and clustering Spatio-Temporal Point Processes Motivating examples A classification of spatio-temporal point patterns and processes Second-order properties Conditioning on the past Empirical and mechanistic models Exploratory Analysis Animation Marginal and conditional summaries Second-order properties Empirical Models and Methods Poisson processes Cox processes Log-Gaussian Cox processes Inference Gastro-intestinal illness in Hampshire, UK Concluding remarks: point processes and geostatistics Mechanistic Models and Methods Conditional intensity and likelihood Partial likelihood The 2001 foot-and-mouth epidemic in Cumbria, UK Nesting patterns of Arctic terns References