Can the Spatial Point Patterns of Animal Distributions Be Detected Using Sparse Samples? A Case Study of Four Soricomorpha (Mammalia) Species in Poland / Czy Przestrzenny Wzorzec Rozkładu Punktów W Dystrybucji Zwierząt Może Zostać Określony Na Podstawie Rzadkiego Próbkowania? Studium Przypadku Na Czterech Gatunkach Soricomorpha (Mammalia) Występujących W Polsce.

In this work, we consider variable selection when modelling the intensity and clustering of inhomogeneous spatial point processes, integrating well‐known procedures in the respective fields of variable selection and spatial point process modelling to introduce a simple procedure for variable selection in spatial point process modelling. Specifically, we consider modelling spatial point data with Poisson, pairwise interaction and Neyman–Scott cluster models, and incorporate LASSO, adaptive LASSO, and elastic net regularization methods into the generalized linear model framework for fitting these point models. We perform simulation studies to explore the effectiveness of using each of the three‐regularization methods in our procedure. We then use the procedure in two applications, modelling the intensity and clustering of rainforest trees with soil and geographical covariates using a Neyman–Scott model, and of fast food restaurant locations in New York City with Census variables and school locations using a pairwise interaction model.The Canadian Journal of Statistics43: 288–305; 2015 © 2015 Statistical Society of Canada

Spatial point process models are theoretically useful for mapping discrete events, such as plant or animal presence, across space; however, the computational complexity of fitting these models is often a barrier to their practical use. The log-Gaussian Cox process (LGCP) is a point process driven by a latent Gaussian field, and recent advances have made it possible to fit Bayesian LGCP models using approximate methods that facilitate rapid computation. These advances include the integrated nested Laplace approximation (INLA) with a stochastic partial differential equations (SPDE) approach to sparsely approximate the Gaussian field and an extension using pseudodata with a Poisson response. To help link the theoretical results to statistical practice, we provide an overview of INLA for point process data and then illustrate their implementation using freely available data. The analyzed datasets include both a completely observed spatial field and an incomplete data situation. Our well-commented R code is shared in the online supplement. Our intent is to make these methods accessible to the practitioner of spatial statistics without requiring deep knowledge of point process theory.

Electric vehicle charging point placement optimisation by exploiting spatial statistics and maximal coverage location models

Multivariate spatial meta kriging

The uncertainty in the locations of vehicles on streets induced by vehicles passing and queueing make the spatial modeling of vehicles a difficult task. To analyze the performance of vehicle-to-vehicle (V2V) communication for vehicular ad hoc networks (VANETs), accurate spatial modeling is of great im-portance. In this paper, we concentrate on spatial point process modeling for random vehicle locations in large and small cities, performing empirical experiments with real location data of mobile taxi trajectories recorded by the global positioning system (GPS) in Beijing city of China and Porto city of Portugal. We find that the empirical probability mass functions (PMFs) of the number of taxis in test sets in different regions of Beijing or in Porto all follow a negative binomial (NB) distribution. Based on the above, we show that the Log Gaussian Cox Process (LGCP) model, whose empirical PMF nicely fits the NB distribution, accurately characterizes diverse spatial point patterns of random vehicle location in both large and small cities. This is verified by the minimum contrast method. The LGCP model can be applied to analyze performance metrics (i.e., connectivity, coverage, and capacity) and optimize the practical deployments of VANETs.

Cellular networks have a great transformation during the last decade. The traditional cellular network system is often overlaid with well-deployed BSs of proper power. However, more and more complex elements such as picocells, femtocells and relays have been introduced to cellular network system. BSs in these elements are unplanned, user-installed and randomly deployed. All of these things compose heterogeneous cellular networks (HCNs). In order to evaluate the performance of HCNs, people usually model the distribution of BSs in HCNs as spatial stochastic point process model. One of the most popular spatial models for these HCNs is Poisson Point Process (PPP) model. However the PPP model is not exact for some cases where BSs in PPP model may be too close to each other. In this paper, we propose a more reasonable and practical model called Matern-like point process (MLPP) model which imposes a certain minimal distance between any two BSs to overcome this problem. Simulations show that the coverage probability of the proposed model noticeably outperforms the PPP model. This improvement depends on the value of minimal distance. We also evaluate the system efficiency defined by the ratio of coverage probability and total power. The results show that the MLPP model has a significant improvement compared to PPP model.

Spatial point processes and neural networks: A convenient couple

栅格计算因其具有简单的构架成为目前地学分析的主流模型，然而，由于栅格计算平均分配计算和存储资源的弱点，不仅容易产生冗余，更重要的是难以凸显研究对象的突变部分，从而使研究者有可能忽略地学现象的变化特征。为此，本文提出将时空点过程模型应用于地学研究。时空点过程不仅适用于模拟以点事件为基本单元的地学现象，而且由于大多数地学过程可以转化为时空点过程，故其具有更广泛的应用范围。因此，时空点过程不仅是一种数据模型，同时也是地学问题的分析方法，更是观察和理解地学问题的一种新视角。为了实现从点过程数据中提取模式，作者经过多年研究提出了时空点过程层次分解理论框架，该理论与信号处理理论中的谱分析思路类似，首先，假设任意点集为有限多个均匀点过程的叠加，然后，通过点局部密度表达工具K阶邻近距离，将空间点转换为混合概率密度函数，再应用优化方法将混合密度函数进行分解得到丛集点和噪声，最终利用密度相连原理从丛集点中提取模式。该理论框架可适用于绝大多数点集数据，初步实现了点集数据的“傅里叶变换”。

Safety applications based on vehicle-to-vehicle (V2V) communication have become a major goal toward the intelligent transportation. The performance of the applications is mainly affected by the communication links, which in turn are governed by the topology characteristics of vehicular ad hoc networks (VANETs). To analyze the performance of V2V communication for VANETs, accurate spatial modeling is of great importance. There is an absence of a widely accepted two-dimensional (2D) model that well characterizes the random vehicle locations; the widely used Poisson point process (PPP) model is simple but not close to reality. In this paper, we concentrate on spatial point process modeling for random vehicle locations in large and small cities, performing empirical experiments with real location data of mobile taxi trajectories recorded by the global positioning system in Beijing city of China and Porto city of Portugal. We find that the empirical probability mass functions (PMFs) of the number of taxis in test sets in different regions of Beijing or in Porto all follow a negative binomial (NB) distribution. The spatial correlations of the points are established by comparing the results of different sampling methods. Based on the above, we show that the Log Gaussian Cox Process (LGCP) model, whose empirical PMF nicely fits the NB distribution, accurately characterizes diverse spatial point patterns of random vehicle location in both large and small cities. This is verified by the minimum contrast method. Then, we study the node degree as an important metric for the communication performance of the networks. It is shown that the connectivity of the LGCP model closely represents the connectivity found in the actual data, for both representative cities. The LGCP model is far more accurate than the widely used one-dimensional models and the 2D PPP for modeling the vehicle distribution, which is significant in V2V communication.

Tree species were assembled into forest communities by various processes, and it was found that trees are spatially arranged in a community by the abiotic and biotic conditions within that community. Here, we explore the abiotic processes and biotic interactions in the spatial patterning of tree species across six old‐growth forest types in a tropical nature reserve. Four spatial point process models (the homogeneous Poisson process, inhomogeneous Poisson process, homogeneous Thomas process, and inhomogeneous Thomas process) were used to evaluate the potential contribution of the random processes, habitat heterogeneity, dispersal limitation, and the joint effects of dispersal and habitat heterogeneity to the formation of the spatial patterns of tree species. A combination of the null model and size–distance regression analysis was applied to assess the effect of competition and facilitation on the tree species assembly. We found that the homogeneous and inhomogeneous Thomas processes were the best models for describing the spatial patterns of more than 85% tree species across the six tropical forests. The combination of the null model and size–distance regression analysis showed that 37–44% of tree species were affected by competition and 9–24% of tree species were affected by facilitation across the six tropical forest types. Competition was the dominant form of species interactions in forests with mild abiotic conditions such as the tropical montane rain forest and tropical lowland rain forest. Meanwhile, facilitation was the most important biotic interaction in the abiotically harsh tropical montane dwarf forest on mountaintops. Our study suggests that dispersal limitation and the joint effects of dispersal and habitat heterogeneity were the dominant abiotic processes in controlling the spatial patterning of trees in tropical forests. Moreover, the relative importance of competition and facilitation in the assembly of the tree species varied among the forest types with different abiotic conditions.

SummaryWe discuss the practice of directly or indirectly assuming a model for the number of points when modelling spatial point patterns even though it is rarely possible to validate such a model in practice because most point pattern data consist of only one pattern. We therefore explore the possibility to condition on the number of points instead when fitting and validating spatial point process models. In a simulation study with different popular spatial point process models, we consider model validation using global envelope tests based on functional summary statistics. We find that conditioning on the number of points will for some functional summary statistics lead to more narrow envelopes and thus stronger tests and that it can also be useful for correcting for some conservativeness in the tests when testing composite hypothesis. However, for other functional summary statistics, it makes little or no difference to condition on the number of points. When estimating parameters in popular spatial point process models, we conclude that for mathematical and computational reasons, it is convenient to assume a distribution for the number of points.

Strategic fire and fuel management planning benefits from detailed understanding of how wildfire occurrences are distributed spatially under current climate, and from predictive models of future wildfire occurrence given climate change scenarios. In this study, we fitted historical wildfire occurrence data from 1986 to 2009 to a suite of spatial point process (SPP) models with a model averaging approach. We then predicted human- and lightning-caused wildfire occurrence over the 2010–2100 period in the Lake Tahoe Basin, a forested watershed in the western US with an extensive wildland–urban interface. The purpose of our research was threefold, including (1) to quantify the influence of biophysical and anthropogenic explanatory variables on spatial patterns of wildfire occurrence, (2) to model current and future spatial distribution of wildfire occurrence under two carbon emission scenarios (A2 and B1), and (3) to assess prediction uncertainty due to model selection. We found that climate variables exerted stronger influences on lightning-caused fires, with climatic water deficit the most important climatic variable for both human- and lightning-caused fires. The recent spatial distribution of wildfire hotspots was mainly constrained by anthropogenic factors because most wildfires were human-caused. The future distribution of hotspots (i.e. places with high fire occurrence density), however, was predicted to shift to higher elevations and ridge tops due to a more rapid increase of lightning-caused fires. Landscape-scale mean fire occurrence density, averaged from our top SPP models with similar empirical support, was predicted to increase by 210% and 70% of the current level under the A2 and B1 scenarios. However, individual top SPP models could lead to substantially different predictions including a small decrease, a moderate increase, and a very large increase, demonstrating the critical need to account for model uncertainty.

Summary1. The need to understand the processes shaping population distributions has resulted in a vast increase in the diversity of spatial wildlife data, leading to the development of many novel analytical techniques that are fit‐for‐purpose. One may aggregate location data into spatial units (e.g. grid cells) and model the resulting counts or presence–absences as a function of environmental covariates. Alternatively, the point data may be modelled directly, by combining the individual observations with a set of random or regular points reflecting habitat availability, a method known as a use‐availability design (or, alternatively a presence – pseudo‐absence or case–control design).2. Although these spatial point, count and presence–absence methods are widely used, the ecological literature is not explicit about their connections and how their parameter estimates and predictions should be interpreted. The objective of this study is to recapitulate some recent statistical results and illustrate that under certain assumptions, each method can be motivated by the same underlying spatial inhomogeneous Poisson point process (IPP) model in which the intensity function is modelled as a log‐linear function of covariates.3. The Poisson likelihood used for count data is a discrete approximation of the IPP likelihood. Similarly, the presence–absence design will approximate the IPP likelihood, but only when spatial units (i.e. pixels) are extremely small (Electric Journal of Statistics, 2010, 4, 1151–1201). For larger pixel sizes, presence–absence designs do not differentiate between one or multiple observations within each pixel, hence leading to information loss.4. Logistic regression is often used to estimate the parameters of the IPP model using point data. Although the response variable is defined as 0 for the availability points, these zeros do not serve as true absences as is often assumed; rather, their role is to approximate the integral of the denominator in the IPP likelihood (The Annals of Applied Statistics, 2010, 4, 1383–1402). Because of this common misconception, the estimated exponential function of the linear predictor (i.e. the resource selection function) is often assumed to be proportional to occupancy. Like IPP and count models, this function is proportional to the expected density of observations.5. Understanding these (dis‐)similarities between different species distribution modelling techniques should improve biological interpretation of spatial models and therefore advance ecological and methodological cross‐fertilization.

The use of object-orientation for both spatial data and spatial process models facilitates their integration, which can allow exploration and explanation of spatial-temporal phenomena. In order to better understand how tight coupling might proceed and to evaluate the possible functional and efficiency gains from such a tight coupling, we identify four key relationships affecting how geographic data (fields and objects) and agent-based process models can interact: identity, causal, temporal and topological. We discuss approaches to implementing tight integration, focusing on a middleware approach that links existing GIS and ABM development platforms, and illustrate the need and approaches with example agent-based models.

This study discusses the theoretical foundation of the application of spatial hedonic approaches—the hedonic approach employing spatial econometrics or/and spatial statistics—to benefits evaluation. The study highlights the limitations of the spatial econometrics approach since it uses a spatial weight matrix that is not employed by the spatial statistics approach. Further, the study presents empirical analyses by applying the Spatial Autoregressive Error Model (SAEM), which is based on the spatial econometrics approach, and the Spatial Process Model (SPM), which is based on the spatial statistics approach. SPMs are conducted based on both isotropy and anisotropy and applied to different mesh sizes. The empirical analysis reveals that the estimated benefits are quite different, especially between isotropic and anisotropic SPM and between isotropic SPM and SAEM; the estimated benefits are similar for SAEM and anisotropic SPM. The study demonstrates that the mesh size does not affect the estimated amount of benefits. Finally, the study provides a confidence interval for the estimated benefits and raises an issue with regard to benefit evaluation.