Spatial Statistics最新文献

In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on asymptotics or on Monte Carlo simulation of a parametric null model. Here, we present a nonparametric test based on resampling the Fry points of the observed point pattern. Empirical levels and powers of the test are investigated in a simulation study for four point process models with anisotropy induced by different mechanisms. Finally, a real data set is tested for isotropy.

Indonesia is a country that has been greatly affected by the Covid-19 pandemic. In the almost three years that the pandemic has been going on, the spread of Covid-19 has penetrated almost all regions of Indonesia. One of the causes of the rapid spread of Covid-19 confirmed cases in Indonesia is the existence of domestic flights between regions within the archipelago. This research is aimed to identify patterns of Covid-19 transmission cases between provinces in Indonesia using spatio-temporal clustering. The method used a generalized lasso approach based on flight connections and proximity between provinces. The results suggested that clustering based on flight connections between provinces obtained more reasonable results, namely that there were three clusters of provinces formed with different patterns of spread of Covid-19 cases over time.

This paper marks the 50-year publication anniversary of Besag's seminal spatial auto- models paper. His classic article synthesizes generic autoregressive specifications (i.e., a response variable appears on both sides of a regression equation and/or probability function equal sign) for the following six popular random variables: normal, logistic (i.e., Bernoulli), binomial, Poisson, exponential, and gamma. Besag dismisses these last two while recognizing failures of both as well as the more scientifically critical counts-oriented auto-Poisson. His initially unsuccessful subsequent work first attempted to repair them (e.g., pseudo-likelihood estimation), and then successfully revise them within the context of mixed models, formulating a spatially structured random effects term that effectively and efficiently absorbs and accounts for spatial autocorrelation in geospatial data. One remaining weakness of all but the auto-normal is a need to resort to Markov chain Monte Carlo (MCMC) techniques for legitimate estimation purposes. Recently, Griffith succeeded in devising an innovative uniform distribution genre—sui-uniform random variables—that accommodates spatial autocorrelation, too. Its most appealing feature is that, by applying two powerful mathematical statistical theorems (i.e., the probability integral transform, and the quantile function), it redeems Besag's auto- model failures. This paper details conversion of Besag's initial six modified variates, exemplifying them with both simulation experiments and publicly accessible real-world georeferenced data. The principal outcome is valuable spatial statistical advancements, with special reference to Moran eigenvector spatial filtering.

Geostatistical regression models are widely used in environmental and geophysical sciences to characterize the mean and dependence structures for spatio-temporal data. Traditionally, these models account for covariates solely in the mean structure, neglecting their potential impact on the spatio-temporal covariance structure. This paper addresses a significant gap in the literature by proposing a novel covariate-dependent covariance model within the spatio-temporal random-effects model framework. Our approach integrates covariates into the covariance function through a Cholesky-type decomposition, ensuring compliance with the positive-definite condition. We employ maximum likelihood for parameter estimation, complemented by an efficient expectation conditional maximization algorithm. Simulation studies demonstrate the superior performance of our method compared to conventional techniques that ignore covariates in spatial covariances. We further apply our model to a PM_2.5 dataset from Taiwan, highlighting wind speed’s pivotal role in influencing the spatio-temporal covariance structure. Additionally, we incorporate wind speed and sunshine duration into the covariance function for analyzing Taiwan ozone data, revealing a more intricate relationship between covariance and these meteorological variables.

To mitigate the negative effects of emerging wildlife diseases in biodiversity and public health it is critical to accurately forecast pathogen dissemination while incorporating relevant spatio-temporal covariates. Forecasting spatio-temporal processes can often be improved by incorporating scientific knowledge about the dynamics of the process using physical models. Ecological diffusion equations are often used to model epidemiological processes of wildlife diseases where environmental factors play a role in disease spread. Physics-informed neural networks (PINNs) are deep learning algorithms that constrain neural network predictions based on physical laws and therefore are powerful forecasting models useful even in cases of limited and imperfect training data. In this paper, we develop a novel ecological modeling tool using PINNs, which fits a feedforward neural network and simultaneously performs parameter identification in a partial differential equation (PDE) with varying coefficients. We demonstrate the applicability of our model by comparing it with the commonly used Bayesian stochastic partial differential equation method and traditional machine learning approaches, showing that our proposed model exhibits superior prediction and forecasting performance when modeling chronic wasting disease in deer in Wisconsin. Furthermore, our model provides the opportunity to obtain scientific insights into spatio-temporal covariates affecting spread and growth of diseases. This work contributes to future machine learning and statistical methodology development by studying spatio-temporal processes enhanced by prior physical knowledge.

Nonstationary and non-Gaussian spatial data are common in various fields, including ecology (e.g., counts of animal species), epidemiology (e.g., disease incidence counts in susceptible regions), and environmental science (e.g., remotely-sensed satellite imagery). Due to modern data collection methods, the size of these datasets have grown considerably. Spatial generalized linear mixed models (SGLMMs) are a flexible class of models used to model nonstationary and non-Gaussian datasets. Despite their utility, SGLMMs can be computationally prohibitive for even moderately large datasets (e.g., 5000 to 100,000 observed locations). To circumvent this issue, past studies have embedded nested radial basis functions into the SGLMM. However, two crucial specifications (knot placement and bandwidth parameters), which directly affect model performance, are typically fixed prior to model-fitting. We propose a novel approach to model large nonstationary and non-Gaussian spatial datasets using adaptive radial basis functions. Our approach: (1) partitions the spatial domain into subregions; (2) employs reversible-jump Markov chain Monte Carlo (RJMCMC) to infer the number and location of the knots within each partition; and (3) models the latent spatial surface using partition-varying and adaptive basis functions. Through an extensive simulation study, we show that our approach provides more accurate predictions than competing methods while preserving computational efficiency. We demonstrate our approach on two environmental datasets - incidences of plant species and counts of bird species in the United States.

In spatial statistics, fast and accurate parameter estimation, coupled with a reliable means of uncertainty quantification, can be challenging when fitting a spatial process to real-world data because the likelihood function might be slow to evaluate or wholly intractable. In this work, we propose using convolutional neural networks to learn the likelihood function of a spatial process. Through a specifically designed classification task, our neural network implicitly learns the likelihood function, even in situations where the exact likelihood is not explicitly available. Once trained on the classification task, our neural network is calibrated using Platt scaling which improves the accuracy of the neural likelihood surfaces. To demonstrate our approach, we compare neural likelihood surfaces and the resulting maximum likelihood estimates and approximate confidence regions with the equivalent for exact or approximate likelihood for two different spatial processes—a Gaussian process and a Brown–Resnick process which have computationally intensive and intractable likelihoods, respectively. We conclude that our method provides fast and accurate parameter estimation with a reliable method of uncertainty quantification in situations where standard methods are either undesirably slow or inaccurate. The method is applicable to any spatial process on a grid from which fast simulations are available.