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Application and Fast Inference Method of Spatial Point Patterns
Abstract
Point pattern data are increasingly common in applied research. While these data are inherently locational, social scientists predominately analyze aggregate summaries of these events as areal data. In so doing, they lose much of the information inherent to these point pattern data, and much of the flexibility that comes from analyzing events using point process models. These adverse impacts motivate our advocacy of spatial point process models for fitting point pattern data. Social scientists have lagged in the adoption of spatial point process models may either be due to a lack of familiarity with them or the high computational cost of estimation. In this dissertation, we aim to help researchers understand and utilize spatial point process models by achieving the following four objectives. First, we review some basic concepts of spatial point process models. Then, we propose a minimum contrast method for inferring multivariate spatial point process models to save the computational cost. The last two objectives are applications of spatial point process models for point pattern data in two fields: political science and meteorology.
The basic concepts reviewed include summary statistics associated with properties of spa-tial point process models (nth order itensities, covariance functions, marginal and cross K functions); and two commonly used spatial point process models (Poisson point process and log-Gaussian Cox process). These basic concepts play an important role in the dissertation, as the focus of this dissertation is conducting inference based on these summary statistics and assessing the properties of interest of spatial point patterns.
Minimum contrast (MC) method is a commonly used inference approach that focuses on the second-order properties of point processes, such as the spatial interaction between points. Its popularity is due to the computationally efficiency relative to likelihood-based methods. This computational advantage becomes even more salient when working with complex point process models. While these practical advantages are well known, there has been little development of MC for multivariate spatial point patterns. Here, we propose a MC method for multivariate spatial point patterns via multivariate K functions and provide a method to select tuning parameters. Further, we study the asymptotic properties of MC estimators of multivariate stationary spatial point processes. Simulation results demonstrate the fast computation and reasonable parameter accuracy of MC (under optimal tuning parameters) compared to Bayesian Markov Chain Monte Carlo (BMCMC). We apply these methods to an analysis of terrorism attacks in Nigeria during 2014 from the Global Terrorism Database (GTD), focusing on bivariate modeling of spatial point patterns of terror attacks by two major groups in the country.
This dissertation also concentrates on fitting spatial point pattern data in different fields with specific research goals. Spatial point pattern data is common in political science research. Recognizing advantages of spatial point process models, applied statisticians have increasingly utilized these models in the analysis of political events. Yet, this work often neglects the inherent limitations of political event data (e.g, geolocation accuracy), which can complicate the direct application of point process models. Here, we attempt to bridge this divide: introducing the benefits of point process modeling for political science research, and highlighting the unique challenges political science data pose for these approaches. To ground our discussion, we focus the GTD, using a univariate and bivariate log-Gaussian Cox process model (LGCP) to analyze terror attacks in Nigeria during 2014.
Another field which would benefit from the use of spatial point process models is in meteorology. Specifically, understanding the causes and distribution patterns of lightning is important, as lighting can spark wildfires, impact the NOx cycle, and even endangers human life. We thus investigate lightning parameterizations based solely on large-scale environmental variables (CSF, CAPE and LCL), which has not been well studied. Here we employs two statistical models, logistic regression (LR) and LGCP, to estimate lightning occurrence and intensity for orbital and seasonal analyses over Brazil in 2018. To evaluate model performance, we plot precision-recall curves (PRC) from LR and LGCP and calculate their area under the curve (AUC). In AUC terms, LGCP outperforms the LR estimator. Once the lightning parameteri-zations are determined, their lightning predictions are further implemented in a global climate model (GCM) which generates current and future seasonal climates (covariates) to study how lightning changes over time. LR and LGCP results both show a similar trend in lightning change over time: decreases in the north and increases in the south, which could provide important implications for environmental changes in the NOx cycle and wildfire frequency.
Subject
Spatial point pattern dataminimum contrast (MC)
multivariate stationary point process
log-Gaussian Cox Process (LGCP)
Citation
Zhu, Lin (2022). Application and Fast Inference Method of Spatial Point Patterns. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /197994.