Inhomogeneous Poisson Point Process Model Research Articles

COVID-19 Death Risk in Surabaya: Modeling by Spatial Point Process

The total death rate or Case Fatality Rate (CFR) due to COVID-19 in Surabaya is high, that is almost twice of the global CFR (1.4%). Utilization of high-resolution data has the potential to explore COVID-19 cases, not only recording cases at the district or city level but also at the patient’s domicile level so that they can provide more detailed spatial information. Meanwhile, research exploring the risk of death from COVID-19, especially in Surabaya using spatial point process model, has not yet been carried out. In this study, an analysis of the risk of death from COVID-19 in Surabaya will be carried out using the inhomogeneous Poisson point process model with covariates or external factors used including the density of the COVID-19 referral hospital location and the proportion of confirmed COVID-19 population aged > 60 years per districts. Our model shows that referral hospitals (exp( ) = 1.03295) and places of worship (exp( ) = 1.03835) have a significant effect on death risk from COVID-19. So, there is a need for special handling for areas that have a population with a vulnerable age (> 60 years) where at this age the human immune system will decrease.
 Keywords: COVID-19, heath risk, spatial point process, surabaya

Inhomogeneous spatio-temporal point processes on linear networks for visitors’ stops data

We analyse the spatio-temporal distribution of visitors’ stops by touristic attractions in Palermo (Italy), using theory of stochastic point processes living on linear networks. We first propose an inhomogeneous Poisson point process model with a separable parametric spatio-temporal first-order intensity. We account for the spatial interaction among points on the given network, fitting a Gibbs point process model with mixed effects for the purely spatial component. This allows us to study first-order and second-order properties of the point pattern, accounting both for the spatio-temporal clustering and interaction and for the spatio-temporal scale at which they operate. Due to the strong degree of clustering in the data, we then formulate a more complex model, fitting a spatio-temporal log-Gaussian Cox process to the point process on the linear network, addressing the problem of the choice of the most appropriate distance metric.

Spatial Relationship Between Eviction Filings, Neighborhood Characteristics, and Proximity to the Central Business District: A Case Study of Salt Lake County, Utah

ABSTRACT There has been an increasing body of literature analyzing eviction in different cities and contexts in urban studies, public health, sociology, geography, and housing studies. Still, little has been known about the underlying spatial point process of how housing evictions are generated. After geocoding eviction filing cases in Salt Lake County in 2015, this study analyzed factors affecting the intensity of eviction using the inhomogeneous Poisson point process (IPP) model. The IPP model result identified demographic, economic, and housing covariates associated with the high intensity of eviction filings. This study also found a significant relationship between eviction filings and the built environment characteristics—such as proximity to central business district (CBD) and light rail transit stations, intersection density, and land use mix score. Particularly, this study found that the intensity of housing evictions is negatively associated with an increase in the distance to CBD when CBD was transformed into gentrified areas led by new high-end apartment constructions during the housing boom since 2000. The article ends with some recommendations for policymakers, including the implementation of an “anti-eviction zone” in CBD areas to reduce the high intensity of housing evictions led by new high-end apartment constructions.

Developing a point process model for ecological risk assessment of pine wilt disease at multiple scales

Pine wilt disease (PWD) is one of the most serious conifer diseases, with further expansion expected under ongoing climate change. Sustainable forest management and effective pest control of pine forests therefore requires rigorous exploration of potential PWD risk areas under current and future climate conditions. To predict potential PWD risk areas in Japan, we constructed an inhomogeneous Poisson point process (IPP) model, which allows the use of strongly biased data. We examined both current and near-future climatic conditions (2026–2050, five general circulation model under two representative concentration pathways [RCPs]). Occurrence data were obtained on three different spatial scales (national, regional and local) along with eight bioclimatic variables. The resultant model was able to correct the data bias caused by using these three different data sources and showed high predictive power as follows: (1) potential risk areas will increase more than the current PWD distribution; (2) mean annual temperature will have the highest effect of the eight predictor variables; (3) high-risk areas will expand northwards and/or upwards in the near future, at a maximum of ca. +58.6% under RCP 8.5 and a minimum of ca. +15.9% under RCP 2.6 and low risk areas will decrease. The high-resolution PWD risk maps created with the IPP model will therefore aid future pest control and forest management strategies at local, regional, and national scales.

Combining multiple data sources in species distribution models while accounting for spatial dependence and overfitting with combined penalized likelihood maximization

Abstract The increase in availability of species datasets means that approaches to species distribution modelling that incorporate multiple datasets are in greater demand. Recent methodological developments in this area have led to combined likelihood approaches, in which a log‐likelihood comprised of the sum of the log‐likelihood components of each data source is maximized. Often, these approaches make use of at least one presence‐only dataset and use the log‐likelihood of an inhomogeneous Poisson point process model in the combined likelihood construction. While these advancements have been shown to improve predictive performance, they do not currently address challenges in presence‐only modelling such as checking and correcting for violations of the independence assumption of a Poisson point process model or more general challenges in species distribution modelling such as overfitting. In this paper, we present an extension of the combined likelihood framework which accommodates alternative presence‐only likelihoods in the presence of spatial dependence as well as lasso‐type penalties to account for potential overfitting. We compare the proposed combined penalized likelihood approach to the standard combined likelihood approach via simulation and apply the method to modelling the distribution of the Eurasian lynx in the Jura Mountains in eastern France. The simulations show that the proposed combined penalized likelihood approach has better predictive performance than the standard approach when spatial dependence is present in the data. The lynx analysis shows that the predicted maps vary significantly between the model fitted with the proposed combined penalized approach accounting for spatial dependence and the model fitted with the standard combined likelihood. This work highlights the benefits of careful consideration of the presence‐only components of the combined likelihood formulation, and allows greater flexibility and ability to accommodate real datasets.

Resource selection by recolonizing American black bears in a fragmented forest landscape

Abstract Following functional extirpation in Missouri, American black bear (Ursus americanus) populations in this state have been increasing in recent years through recolonization from re-established populations in northern Arkansas. To increase our understanding of resource selection by recolonizing black bears in the Ozark Highlands of the United States, we attached Global Positioning System (GPS) transmitters to 54 black bears during May–August 2010–2013, and used location data based on biological seasons. We constructed models with anthropogenic (distance to nearest development, distance to nearest road), biological (sex, age class, season), and environmental (distance to nearest water, land cover) categories. We used infinitely weighted logistic regression to approximate the inhomogeneous Poisson point process model for presence-only (i.e., GPS locations) data to fit models. We used Bayesian Information Criterion and found that the best-performing model in the set of 81 models included all independen...

Kernel Intensity Estimation of 2-Dimensional Spatial Poisson Point Processes From k-Tree Sampling

To estimate the spatial intensity (density) of plants and animals, ecologists often sample populations by prespecifing a spatial array of points, then measuring the distance from each point to the k nearest organisms, a so-called k-tree sampling method. A variety of ad hoc methods are available for estimating intensity from k-tree sampling data, but they assume that two distinct points of the array do not share nearest neighbors. However, nearest neighbors are likely to be shared when the population intensity is low, as it is in our application. The purpose of this paper is twofold: (a) to derive and use for estimation the likelihood function for a k-tree sample under an inhomogeneous Poisson point-process model and (b) to estimate spatial intensity when nearest neighbors are shared. We derive the likelihood function for an inhomogeneous Poisson point-process with intensity λ(x,y) and propose a likelihood-based, kernel-smoothed estimator $\hat{\lambda}(x,y)$ . Performance of the method for k=1 is tested on four types of simulated populations: two homogeneous populations with low and high intensity, a population simulated from a bivariate normal distribution of intensity, and a “cliff” population in which the region is divided into high- and low-intensity subregions. The method correctly detected spatial variation in intensity across different subregions of the simulated populations. Application to 1-tree samples of carnivorous pitcher plants populations in four New England peat bogs suggests that the method adequately captures empirical patterns of spatial intensity. However, our method suffers from two evident sources of bias. First, like other kernel smoothers, it underestimates peaks and overestimates valleys. Second, it has positive bias analogous to that of the MLE for the rate parameter of exponential random variables.

Nondetection sampling bias in marked presence‐only data

Species distribution models (SDM) are tools used to determine environmental features that influence the geographic distribution of species' abundance and have been used to analyze presence-only records. Analysis of presence-only records may require correction for nondetection sampling bias to yield reliable conclusions. In addition, individuals of some species of animals may be highly aggregated and standard SDMs ignore environmental features that may influence aggregation behavior.We contend that nondetection sampling bias can be treated as missing data. Statistical theory and corrective methods are well developed for missing data, but have been ignored in the literature on SDMs. We developed a marked inhomogeneous Poisson point process model that accounted for nondetection and aggregation behavior in animals and tested our methods on simulated data.Correcting for nondetection sampling bias requires estimates of the probability of detection which must be obtained from auxiliary data, as presence-only data do not contain information about the detection mechanism. Weighted likelihood methods can be used to correct for nondetection if estimates of the probability of detection are available. We used an inhomogeneous Poisson point process model to model group abundance, a zero-truncated generalized linear model to model group size, and combined these two models to describe the distribution of abundance. Our methods performed well on simulated data when nondetection was accounted for and poorly when detection was ignored.We recommend researchers consider the effects of nondetection sampling bias when modeling species distributions using presence-only data. If information about the detection process is available, we recommend researchers explore the effects of nondetection and, when warranted, correct the bias using our methods. We developed our methods to analyze opportunistic presence-only records of whooping cranes (Grus americana), but expect that our methods will be useful to ecologists analyzing opportunistic presence-only records of other species of animals.

Comparative interpretation of count, presence–absence and point methods for species distribution models

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.

A Conditional Approach to Point Process Modelling of Elevated Risk

SUMMARY We consider the problem of investigating the elevation in risk for a specified disease in relation to possible environmental factors. Our starting point is an inhomogeneous Poisson point process model for the spatial variation in the incidence of cases and controls in a designated geographic region, as proposed by Diggle. We develop a conditional approach to inference which converts the point process model to a non-linear binary regression model for the spatial variation in risk. Simulations suggest that the usual asymptotic approximations for likelihood-based inference are more reliable in this conditional setting than in the original point process setting. We present an application to some data on the spatial distribution of asthma in relation to three industrial locations.