Spatial Statistics最新文献

Methods for population estimation and inference have evolved over the past decade to allow for the incorporation of spatial information when using capture–recapture study designs. Traditional approaches to specifying spatial capture–recapture (SCR) models often rely on an individual-based detection function that decays as a detection location is farther from an individual’s activity center. Traditional SCR models are intuitive because they incorporate mechanisms of animal space use based on their assumptions about activity centers. We modify the SCR model to accommodate a wide range of space use patterns, including for those individuals that may exhibit traditional elliptical utilization distributions. Our approach uses underlying Gaussian processes to characterize the space use of individuals. This allows us to account for multimodal and other complex space use patterns that may arise due to movement. We refer to this class of models as geostatistical capture–recapture (GCR) models. We adapt a recursive computing strategy to fit GCR models to data in stages, some of which can be parallelized. This technique facilitates implementation and leverages modern multicore and distributed computing environments. We demonstrate the application of GCR models by analyzing both simulated data and a data set involving capture histories of snowshoe hares in central Colorado, USA.

Commonly, observations from environmental processes are spatially structured and present skewed distributions. Recently, different models have been proposed to model spatial processes in their original scale. This work was motivated by modeling the levels of arsenic groundwater concentration in Comilla, a district of Bangladesh. Some of the observations are left censored. We propose spatial gamma models and explore different parametrizations of the gamma distribution. The gamma model naturally accounts for the skewness present in the data and the fact that arsenic levels are positive. We compare our proposed approaches with two skewed models proposed in the literature. Inference is performed under the Bayesian paradigm and interpolation to unobserved locations of interest naturally accounts for the estimation of the parameters in the proposed model. For the arsenic dataset, one of our proposed gamma models performs best in comparison to previous spatial models for skewed data, in terms of scoring rules criteria. Moreover, under the skewed models, some of the lower limits of the 95% posterior predictive distributions provide negative values violating the assumption that observations are strictly positive. The gamma distribution provides a reasonable, and simpler, alternative to account for the skewness present in the data and provide forecasts that are within the valid values of the observations.

Spatial stratified heterogeneity, revealing the disparity mechanisms across spatial strata, can be effectively quantified using the geographical detector (GD). GD requires reasonable spatial discretization strategies to investigate the spatial association between the target variable and numerical independent variables. In previous studies, the Robust Geographical Detector (RGD) optimized spatial strata for examining the power of determinants (PD) of individual variables, which demonstrate more robust spatial discretization than other models. However, the GD's interaction detector that explores PD of the interaction of two variables still needs to be enhanced by the robust spatial discretization. This study develops a Robust Interaction Detector (RID), an improved interaction detector, using change detection algorithms for the robust spatial stratified heterogeneity analysis with multiple explanatory variables. RID is applied in a road life expectancy analysis in Western Australia. Results show that RID presents higher PD values than previous GD models, ensuring the growth of PD value with more spatial strata. The RID model indicates that the interactions between various transport variables and elevation are strongly associated with road life expectancy from the perspective of spatial patterns. The developed RID model provides significant potential for enhanced geospatial factor analysis across diverse fields.

In recent decades, spatial classification has received considerable attention in a wide array of disciplines. In practice, binary response variable is often subject to measurement error, misclassification. To account for the misclassified response in spatial classification, we proposed validation data-based adjustment methods that use interval validation data to rectify misclassified responses. Regression calibration and multiple imputation methods are utilized to correct the misclassified outcomes at the locations where the gold-standard device is not available. Generalized linear mixed model and indicator Kriging are applied for spatial classification at unsampled locations. Simulation studies are performed to compare the proposed methods with naive methods that ignore the misclassification. It was found that the proposed models significantly improve prediction accuracy. Additionally, the proposed models are applied for precipitation detection in South Korea.

As global temperatures continue to rise, climate mitigation strategies such as stratospheric aerosol injections (SAI) are increasingly discussed, but the downstream effects of these strategies are not well understood. As such, there is interest in developing statistical methods to quantify the evolution of climate variable relationships during the time period surrounding an SAI. Feature importance applied to echo state network (ESN) models has been proposed as a way to understand the effects of SAI using a data-driven model. This approach depends on the ESN fitting the data well. If not, the feature importance may place importance on features that are not representative of the underlying relationships. Typically, time series prediction models such as ESNs are assessed using out-of-sample performance metrics that divide the times series into separate training and testing sets. However, this model assessment approach is geared towards forecasting applications and not scenarios such as the motivating SAI example where the objective is using a data driven model to capture variable relationships. In this paper, we demonstrate a novel use of climate model replicates to investigate the applicability of the commonly used repeated hold-out model assessment approach for the SAI application. Simulations of an SAI are generated using a simplified climate model, and different initialization conditions are used to provide independent training and testing sets containing the same SAI event. The climate model replicates enable out-of-sample measures of model performance, which are compared to the single time series hold-out validation approach. For our case study, it is found that the repeated hold-out sample performance is comparable, but conservative, to the replicate out-of-sample performance when the training set contains enough time after the aerosol injection.

This paper considers a filter for smoothing spatial data. It can be used to smooth data on the vertices of arbitrary undirected graphs with arbitrary non-negative spatial weights. It consists of a quantity analogous to Geary’s $c$, which is one of the most prominent measures of spatial autocorrelation. In addition, the quantity can be represented by a matrix called the graph Laplacian in spectral graph theory. We show mathematically how spatial data becomes smoother as a parameter, called the smoothing parameter, increases from 0 and is fully smoothed as the parameter goes to infinity, except for the case where the spatial data is originally fully smoothed. We also illustrate the results numerically and apply the spatial filter to climatological/meteorological data. In addition, as supplementary investigations, we examine how the sum of squared residuals and the effective degrees of freedom vary with the smoothing parameter. Finally, we review two closely related literatures to the spatial filter. One is the intrinsic conditional autoregressive model and the other is the eigenvector spatial filter. We clarify how the spatial filter considered in this paper relates to them. We then mention future research.

Recent wildfires in Australia have led to considerable economic loss and property destruction, and there is increasing concern that climate change may exacerbate their intensity, duration, and frequency. Hazard quantification for extreme wildfires is an important component of wildfire management, as it facilitates efficient resource distribution, adverse effect mitigation, and recovery efforts. However, although extreme wildfires are typically the most impactful, both small and moderate fires can still be devastating to local communities and ecosystems. Therefore, it is imperative to develop robust statistical methods to reliably model the full distribution of wildfire spread. We do so for a novel dataset of Australian wildfires from 1999 to 2019, and analyse monthly spread over areas approximately corresponding to Statistical Areas Level 1 and 2 (SA1/SA2) regions. Given the complex nature of wildfire ignition and spread, we exploit recent advances in statistical deep learning and extreme value theory to construct a parametric regression model using graph convolutional neural networks and the extended generalised Pareto distribution, which allows us to model wildfire spread observed on an irregular spatial domain. We highlight the efficacy of our newly proposed model and perform a wildfire hazard assessment for Australia and population-dense communities, namely Tasmania, Sydney, Melbourne, and Perth.

Spatial autoregressive model is widely concerned in the economic field, whereas when the data is missing, variable selection and parameter estimation of the model is quite challenging. Based on this, we discuss the variable selection in spatial autoregressive model with missing data. Under the condition that errors are independent and identically distributed, we have developed a penalized quasi-maximum likelihood method to achieve variable selection and parameter estimation simultaneously in the presence of missing responses. The method’s theoretical properties, including consistency and asymptotical normality, are established under certain assumptions. Meanwhile, an improved expectation–maximization algorithm is provided for optimizing the penalized quasi-maximum likelihood function. Simulations are conducted to examine the proposed method and assess the finite-sample performance. Additionally, we present a practical example to illustrate the method’s application.

Georeferenced data often contain missing values, and such missing values can considerably affect spatial modeling. A spatial location model can also suffer from this issue when there are missing values in its geographic distribution of weights. Although general imputation approaches have been developed, one distinguishing fact here is that spatial imputation generally performs better for georeferenced data because it can reflect a fundamental property of those data, that is, spatial autocorrelation or spatial dependency. This paper explores how spatial imputation exploiting spatial autocorrelation can contribute to estimating missing values in a weights surface for location modeling and subsequently improve solutions for spatial optimization, specifically p-median problems using a spatially imputed weights surface. This paper examines two spatial imputation methods, ordinary co-kriging and Moran eigenvector spatial filtering. Their results are compared with conventional linear regression, essentially Expectation-Maximization algorithm results for independent observations of Gaussian random variable cases. Simulation experiments show that spatial imputation produces better results for georeferenced data than simply ignoring any missing values and non-spatial imputation, and appropriately imputed values can enhance spatial optimization solutions, regardless of the number of medians, p.

Spatial areal models encounter the well-known and challenging problem of spatial confounding. This issue makes it arduous to distinguish between the impacts of observed covariates and spatial random effects. Despite previous research and various proposed methods to tackle this problem, finding a definitive solution remains elusive. In this paper, we propose a simplified version of the spatial+ approach that involves dividing the covariate into two components. One component captures large-scale spatial dependence, while the other accounts for short-scale dependence. This approach eliminates the need to separately fit spatial models for the covariates. We apply this method to analyse two forms of crimes against women, namely rapes and dowry deaths, in Uttar Pradesh, India, exploring their relationship with socio-demographic covariates. To evaluate the performance of the new approach, we conduct extensive simulation studies under different spatial confounding scenarios. The results demonstrate that the proposed method provides reliable estimates of fixed effects and posterior correlations between different responses.