Showing papers in "spatial statistics in 2022"

The Spillover Effects of Institutional Quality and Economic Openness on Economic Growth for the Belt and Road Initiative (BRI) countries

Abstract: Several studies have been conducted to investigate the factors that influence Economic Growth (EG). However, the spatial impact of Institutional Quality (IQ) and Economic Openness (EO) was primarily disregarded, especially in BRI countries; only a few research offered proof of institutions’ involvement in boosting economic development. In this article, we increase the existing research on whether neighboring countries’ EO and institutions may also affect EG. Thus, we examine the spillover impact of IQ and EO on EG in a panel of 86 BRI economies over the period 1995–2019 using a Spatial econometric model. Our findings first prove the existence of spatial dependence in EG across nations. Secondly, the results also provide an indication of indirect institutional and EO spillovers. Institutions and EO inside a country contribute to its prosperity and growth and, as a result, have a beneficial spillover impact on the economic development of its neighbors. The BRI policy positive spillover effect on EG in the BRI allied countries and, consequently, create positive spillover effects on the economic development of neighbors. The best model is interpreted with a direct and indirect impact. Finally, the study ends with various policy recommendations for BRI nations regarding the effects of institutions, EO, and spillovers on growth.

A spatio-temporal model based on discrete latent variables for the analysis of COVID-19 incidence

Abstract: We propose a model based on discrete latent variables, which are spatially associated and time specific, for the analysis of incident cases of SARS-CoV-2 infections. We assume that for each area the sequence of latent variables across time follows a Markov chain with initial and transition probabilities that also depend on latent variables in neighboring areas. The model is estimated by a Markov chain Monte Carlo algorithm based on a data augmentation scheme, in which the latent states are drawn together with the model parameters for each area and time. As an illustration we analyze incident cases of SARS-CoV-2 collected in Italy at regional level for the period from February 24, 2020, to January 17, 2021, corresponding to 48 weeks, where we use number of swabs as an offset. Our model identifies a common trend and, for every week, assigns each region to one among five distinct risk groups.

Spatio-temporal modelling of COVID-19 incident cases using Richards’ curve: An application to the Italian regions

Abstract: We introduce an extended generalised logistic growth model for discrete outcomes, in which spatial and temporal dependence are dealt with the specification of a network structure within an Auto-Regressive approach. A major challenge concerns the specification of the network structure, crucial to consistently estimate the canonical parameters of the generalised logistic curve, e.g. peak time and height. We compared a network based on geographic proximity and one built on historical data of transport exchanges between regions. Parameters are estimated under the Bayesian framework, using Stan probabilistic programming language. The proposed approach is motivated by the analysis of both the first and the second wave of COVID-19 in Italy, i.e. from February 2020 to July 2020 and from July 2020 to December 2020, respectively. We analyse data at the regional level and, interestingly enough, prove that substantial spatial and temporal dependence occurred in both waves, although strong restrictive measures were implemented during the first wave. Accurate predictions are obtained, improving those of the model where independence across regions is assumed.

Quantifying the small-area spatio-temporal dynamics of the Covid-19 pandemic in Scotland during a period with limited testing capacity

Abstract: Modelling the small-area spatio-temporal dynamics of the Covid-19 pandemic is of major public health importance, because it allows health agencies to better understand how and why the virus spreads. However, in Scotland during the first wave of the pandemic testing capacity was severely limited, meaning that large numbers of infected people were not formally diagnosed as having the virus. As a result, data on confirmed cases are unlikely to represent the true infection rates, and due to the small numbers of positive tests these data are not available at the small-area level for confidentiality reasons. Therefore to estimate the small-area dynamics in Covid-19 incidence this paper analyses the spatio-temporal trends in telehealth data relating to Covid-19, because during the first wave of the pandemic the public were advised to call the national telehealth provider NHS 24 if they experienced symptoms of the virus. Specifically, we propose a multivariate spatio-temporal correlation model for modelling the proportions of calls classified as either relating to Covid-19 directly or having related symptoms, and provide software for fitting the model in a Bayesian setting using Markov chain Monte Carlo simulation. The model was developed in partnership with the national health agency Public Health Scotland, and here we use it to analyse the spatio-temporal dynamics of the first wave of the Covid-19 pandemic in Scotland between March and July 2020, specifically focusing on the spatial variation in the peak and the end of the first wave.

Bayesian disease mapping: Past, present, and future

Abstract: On the occasion of the Spatial Statistics' 10th Anniversary, I reflect on the past and present of Bayesian disease mapping and look into its future. I focus on some key developments of models, and on recent evolution of multivariate and adaptive Gaussian Markov random fields and their impact and importance in disease mapping. I reflect on Bayesian disease mapping as a subject of spatial statistics that has advanced to date, and continues to grow, in scope and complexity alongside increasing needs of analytic tools for contemporary health science research, such as spatial epidemiology, population and public health, and medicine. I illustrate (potential) utility and impact of some of the disease mapping models and methods for analysing and monitoring communicable disease such as the COVID-19 infection risks during an ongoing pandemic.

Spatial statistics and soil mapping: A blossoming partnership under pressure

Abstract: For the better part of the 20th century pedologists mapped soil by drawing boundaries between different classes of soil which they identified from survey on foot or by vehicle, supplemented by air-photo interpretation, and backed by an understanding of landscape and the processes by which soil is formed. Its limitations for representing gradual spatial variation and predicting conditions at unvisited sites became evident, and in the 1980s the introduction of geostatistics and specifically ordinary kriging revolutionized thinking and to a large extent practice. Ordinary kriging is based solely on sample data of the variable of interest—it takes no account of related covariates. The latter were incorporated from the 1990s onward as fixed effects and incorporated as regression predictors, giving rise to kriging with external drift and regression kriging. Simultaneous estimation of regression coefficients and variogram parameters is best done by residual maximum likelihood estimation. In recent years machine learning has become feasible for predicting soil conditions from huge sets of environmental data obtained from sensors aboard satellites and other sources to produce digital soil maps. The techniques are based on classification and regression, but they take no account of spatial correlations. Further, they are effectively ‘black boxes’; they lack transparency, and their output needs to be validated if they are to be trusted. They undoubtedly have merit; they are here to stay. They too, however, have their shortcomings when applied to spatial data, which spatial statisticians can help overcome. Spatial statisticians and pedometricians still have much to do to incorporate uncertainty into digital predictions, spatial averages and totals over regions, and to take into account errors in measurement and spatial positions of sample data. They must also communicate their understanding of these uncertainties to end users of soil maps, by whatever means they are made.

Bayesian spatio-temporal joint disease mapping of Covid-19 cases and deaths in local authorities of England

Abstract: The overwhelming spatio-temporal nature of the spread of the ongoing Covid-19 pandemic demands urgent attention of data analysts and model developers. Modelling results obtained from analytical tool development are essential to understand the ongoing pandemic dynamics with a view to helping the public and policy makers. The pandemic has generated data on a huge number of interesting statistics such as the number of new cases, hospitalisations and deaths in many spatio-temporal resolutions for the analysts to investigate. The multivariate nature of these data sets, along with the inherent spatio-temporal dependencies, poses new challenges for modellers. This article proposes a two-stage hierarchical Bayesian model as a joint bivariate model for the number of cases and deaths observed weekly for the different local authority administrative regions in England. An adaptive model is proposed for the weekly Covid-19 death rates as part of the joint bivariate model. The adaptive model is able to detect possible step changes in death rates in neighbouring areas. The joint model is also used to evaluate the effects of several socio-economic and environmental covariates on the rates of cases and deaths. Inclusion of these covariates points to the presence of a north-south divide in both the case and death rates. Nitrogen dioxide, the only air pollution measure used in the model, is seen to be significantly positively associated with the number cases, even in the presence of the spatio-temporal random effects taking care of spatio-temporal dependencies present in the data. The proposed models provide excellent fits to the observed data and are seen to perform well for predicting the location specific number of deaths a week in advance. The structure of the models is very general and the same framework can be used for modelling other areally aggregated temporal statistics of the pandemics, e.g. the rate of hospitalisation.

Endemic–epidemic models to understand COVID-19 spatio-temporal evolution

Abstract: We propose an endemic–epidemic model: a negative binomial space–time autoregression, which can be employed to monitor the contagion dynamics of the COVID-19 pandemic, both in time and in space. The model is exemplified through an empirical analysis of the provinces of northern Italy, heavily affected by the pandemic and characterized by similar non-pharmaceutical policy interventions.

Application of Bayesian spatial-temporal models for estimating unrecognized COVID-19 deaths in the United States

Abstract: In the United States, COVID-19 has become a leading cause of death since 2020. However, the number of COVID-19 deaths reported from death certificates is likely to represent an underestimate of the total deaths related to SARS-CoV-2 infections. Estimating those deaths not captured through death certificates is important to understanding the full burden of COVID-19 on mortality. In this work, we explored enhancements to an existing approach by employing Bayesian hierarchical models to estimate unrecognized deaths attributed to COVID-19 using weekly state-level COVID-19 viral surveillance and mortality data in the United States from March 2020 to April 2021. We demonstrated our model using those aged ≥85 years who died. First, we used a spatial-temporal binomial regression model to estimate the percent of positive SARS-CoV-2 test results. A spatial-temporal negative-binomial model was then used to estimate unrecognized COVID-19 deaths by exploiting the spatial-temporal association between SARS-CoV-2 percent positive and all-cause mortality counts using an excess mortality approach. Computationally efficient Bayesian inference was accomplished via the Polya-Gamma representation of the binomial and negative-binomial models. Among those aged ≥85 years, we estimated 58,200 (95% CI: 51,300, 64,900) unrecognized COVID-19 deaths, which accounts for 26% (95% CI: 24%, 29%) of total COVID-19 deaths in this age group. Our modeling results suggest that COVID-19 mortality and the proportion of unrecognized deaths among deaths attributed to COVID-19 vary by time and across states.

Modelling the effect of a border closure between Switzerland and Italy on the spatiotemporal spread of COVID-19 in Switzerland.

Abstract: We present an approach to extend the endemic-epidemic (EE) modelling framework for the analysis of infectious disease data. In its spatiotemporal formulation, spatial dependencies have originally been captured by static neighbourhood matrices. These weight matrices are adjusted over time to reflect changes in spatial connectivity between geographical units. We illustrate this extension by modelling the spread of COVID-19 disease between Swiss and bordering Italian regions in the first wave of the COVID-19 pandemic. The spatial weights are adjusted with data describing the daily changes in population mobility patterns, and indicators of border closures describing the state of travel restrictions since the beginning of the pandemic. These time-dependent weights are used to fit an EE model to the region-stratified time series of new COVID-19 cases. We then adjust the weight matrices to reflect two counterfactual scenarios of border closures and draw counterfactual predictions based on these, to retrospectively assess the usefulness of border closures. Predictions based on a scenario where no closure of the Swiss-Italian border occurred increased the number of cumulative cases in Switzerland by a factor of 2.7 (10th to 90th percentile: 2.2 to 3.6) over the study period. Conversely, a closure of the Swiss-Italian border two weeks earlier than implemented would have resulted in only a 12% (8% to 18%) decrease in the number of cases and merely delayed the epidemic spread by a couple of weeks. Our study provides useful insight into modelling the effect of epidemic countermeasures on the spatiotemporal spread of COVID-19.

Spatial-temporal generalized additive model for modeling COVID-19 mortality risk in Toronto, Canada

Abstract: This article presents a spatial-temporal generalized additive model for modeling geo-referenced COVID-19 mortality data in Toronto, Canada. A range of factors and spatial-temporal terms are incorporated into the model. The non-linear and interactive effects of the neighborhood-level factors, i.e., population density and average of income, are modeled as a two-dimensional spline smoother. The change of spatial pattern over time is modeled as a three-dimensional tensor product smoother. By fitting this model, the space-time effect can uncover the underlying spatial-temporal pattern that is not explained by the covariates. The performance of the modeling method based on the individual data is also compared to the modeling methods based on the aggregated data in terms of in-sample and out-of-sample predictive checking. The results suggest that the individual-level based analysis provided a better overall model fit and higher predictive accuracy for detecting epidemic peaks in this application as compared to the analysis based on the aggregated data.

Spatial robust fuzzy clustering of COVID 19 time series based on B-splines

Abstract: The aim of the work is to identify a clustering structure for the 20 Italian regions according to the main variables related to COVID-19 pandemic. Data are observed over time, spanning from the last week of February 2020 to the first week of February 2021. Dealing with geographical units observed at several time occasions, the proposed fuzzy clustering model embedded both space and time information. Properly, an Exponential distance-based Fuzzy Partitioning Around Medoids algorithm with spatial penalty term has been proposed to classify the spline representation of the time trajectories. The results show that the heterogeneity among regions along with the spatial contiguity is essential to understand the spread of the pandemic and to design effective policies to mitigate the effects.

Fully nonseparable Gneiting covariance functions for multivariate space–time data

Abstract: We broaden the well-known Gneiting class of space–time covariance functions by introducing a very general parametric class of fully nonseparable direct and cross-covariance functions for multivariate random fields, where each component has a spatial covariance function from the Matérn family with its own smoothness and scale parameters and, unlike most of currently available models, its own correlation function in time. We present sufficient conditions that result in valid models with varying degrees of complexity and we discuss the parameterization of those. Continuous-in-space and discrete-in-time simulation algorithms are also given, which are not limited by the number of target spatial coordinates and allow tens of thousands of time coordinates. The application of the proposed model is illustrated on a weather trivariate dataset over France. Our new model yields better fitting and better predictive scores in time compared to a more parsimonious model with a common temporal correlation function.

Clustering spatio-temporal series of confirmed COVID-19 deaths in Europe

Abstract: The impact of the COVID-19 pandemic varied significantly across different countries, with important consequences in the definition of control and response strategies. In this work, to investigate the heterogeneity of this crisis, we analyse the spatial patterns of deaths attributed to COVID-19 in several European countries. To this end, we propose a Bayesian nonparametric approach, based on mixture of Gaussian processes coupled with Dirichlet process, to group the COVID-19 mortality curves. The model provides a flexible framework for the analysis of time series data, allowing the inclusion in the clustering procedure of different features of the series, such as spatial correlations, time varying parameters and measurement errors. We evaluate the proposed methodology on the death counts recorded at NUTS-2 regional level for several European countries in the period from March 2020 to February 2021.

Community mobility in the European regions during COVID-19 pandemic: A partitioning around medoids with noise cluster based on space–time autoregressive models

Abstract: In this paper we propose a robust fuzzy clustering model, the STAR-based Fuzzy C-Medoids Clustering model with Noise Cluster, to define territorial partitions of the European regions (NUTS2) according to the workplaces mobility trends for places of work provided by Google with reference to the whole COVID-19 pandemic period. The clustering model takes into account both temporal and spatial information by means of the autoregressive temporal and spatial coefficients of the STAR model. The proposed clustering model through the noise cluster is capable of neutralizing the negative effects of noisy data. The main empirical results regard the expected direct relationship between the Community mobility trend and the lockdown periods, and a clear spatial interaction effect among neighboring regions.

Spatiotemporal variable selection and air quality impact assessment of COVID-19 lockdown

Abstract: During the first wave of the COVID-19 pandemics in 2020, lockdown policies reduced human mobility in many countries globally. This significantly reduces car traffic-related emissions. In this paper, we consider the impact of the Italian restrictions (lockdown) on the air quality in the Lombardy Region. In particular, we consider public data on concentrations of particulate matters (PM10 and PM2.5) and nitrogen dioxide, pre/during/after lockdown. To reduce the effect of confounders, we use detailed regression function based on meteorological, land and calendar information. Spatial and temporal correlations are handled using a multivariate spatiotemporal model in the class of hidden dynamic geostatistical models (HDGM). Due to the large size of the design matrix, variable selection is made using a hybrid approach coupling the well known LASSO algorithm with the cross-validation performance of HDGM. The impact of COVID-19 lockdown is heterogeneous in the region. Indeed, there is high statistical evidence of nitrogen dioxide concentration reductions in metropolitan areas and near trafficked roads where also PM10 concentration is reduced. However, rural, industrial, and mountain areas do not show significant reductions. Also, PM2.5 concentrations lack significant reductions irrespective of zone. The post-lockdown restart shows unclear results.

Measurement error-filtered machine learning in digital soil mapping

Abstract: This paper presents a two-stage maximum likelihood framework to deal with measurement errors in digital soil mapping (DSM) when using a machine learning (ML) model. The framework is implemented with random forest and projection pursuit regression to illustrate two different areas of machine learning, i.e. ensemble learning with trees and feature-learning. In our proposed framework, a measurement error variance (MEV) is incorporated as a weight in the log-likelihood function so that measurements with a larger MEV receive less weight when a ML model is calibrated. We evaluate the performance of the error-filtered ML models with an error-filtered regression kriging model, in a comprehensive simulation study and in a real-world case study of Namibian data. From the results we show that prediction accuracy can be increased by using our proposed framework, especially when the MEVs are large and heterogeneous.

Higher-dimensional spatial extremes via single-site conditioning

Abstract: Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial extreme value theory based on the conditional multivariate extreme value model, whereby the limit theory is formed through conditioning upon the value at a particular site being extreme. The ensuing methodology allows for a flexible class of dependence structures, as well as models that can be fitted in high dimensions. To overcome issues of conditioning on a single site, we suggest a joint inference scheme based on all observation locations, and implement an importance sampling algorithm to provide spatial realizations and estimates of quantities conditioning upon the process being extreme at any of one of an arbitrary set of locations. The modelling approach is applied to Australian summer temperature extremes, permitting assessment of the spatial extent of high temperature events over the continent.

A D-vine copula-based quantile regression model with spatial dependence for COVID-19 infection rate in Italy

Abstract: The main determinants of COVID-19 spread in Italy are investigated, in this work, by means of a D-vine copula based quantile regression. The outcome is the COVID-19 cumulative infection rate registered on October 30th 2020, with reference to the 107 Italian provinces, and it is regressed on some covariates of interest accounting for medical, environmental and demographic factors. To deal with the issue of spatial autocorrelation, the D-vine copula based quantile regression also embeds a spatial autoregressive component that controls for the extent of spatial dependence. The use of vine copula enhances model flexibility accounting for non-linear relationships and tail dependencies. Moreover, the model selection procedure leads to parsimonious models providing a rank of covariates based on their explanatory power with respect to the outcome.

An interaction Neyman–Scott point process model for coronavirus disease-19

Abstract: With rapid transmission, the coronavirus disease 2019 (COVID-19) has led to over three million deaths worldwide, posing significant societal challenges. Understanding the spatial patterns of patient visits and detecting local cluster centers are crucial to controlling disease outbreaks. We analyze COVID-19 contact tracing data collected from Seoul, which provide a unique opportunity to understand the mechanism of patient visit occurrence. Analyzing contact tracing data is challenging because patient visits show strong clustering patterns, while cluster centers may have complex interaction behavior. Cluster centers attract each other at mid-range distances because other cluster centers are likely to appear in nearby regions. At the same time, they repel each other at too small distances to avoid merging. To account for such behaviors, we develop a novel interaction Neyman-Scott process that regards the observed patient visit events as offsprings generated from a parent cluster center. Inference for such models is challenging since the likelihood involves intractable normalizing functions. To address this issue, we embed an auxiliary variable algorithm into our Markov chain Monte Carlo. We fit our model to several simulated and real data examples under different outbreak scenarios and show that our method can describe the spatial patterns of patient visits well. We also provide useful visualizations that can inform public health interventions for infectious diseases, such as social distancing.

Capturing spatial dependence of COVID-19 case counts with cellphone mobility data

Abstract: Spatial dependence is usually introduced into spatial models using some measure of physical proximity. When analysing COVID-19 case counts, this makes sense as regions that are close together are more likely to have more people moving between them, spreading the disease. However, using the actual number of trips between each region may explain COVID-19 case counts better than physical proximity. In this paper, we investigate the efficacy of using telecommunications-derived mobility data to induce spatial dependence in spatial models applied to two Spanish communities' COVID-19 case counts. We do this by extending Besag York Mollié (BYM) models to include both a physical adjacency effect, alongside a mobility effect. The mobility effect is given a Gaussian Markov random field prior, with the number of trips between regions as edge weights. We leverage modern parametrizations of BYM models to conclude that the number of people moving between regions better explains variation in COVID-19 case counts than physical proximity data. We suggest that this data should be used in conjunction with physical proximity data when developing spatial models for COVID-19 case counts.

Spatial autocorrelation informed approaches to solving location–allocation problems

Abstract: Surveying programs of study at institutions of higher learning throughout the world reveals that one natural disciplinary coupling is statistics and operations research, although these two specific disciplines currently lack an active synergistic research interface. Similarly, the development of spatial statistics and spatial optimization has occurred in parallel and nearly in isolation. This paper seeks to alter this situation by initiating transformative work at the interface of these two subdisciplines, encouraging considerably more future interaction between them. It outlines three ways spatial statistics can contribute to spatial optimization by exploiting spatial autocorrelation in georeferenced data: missing attribute value imputation (analogous to kriging); identifying colocations of local spatial autocorrelation hot spots and spatial medians; and, geographic tessellation stratified random sampling inputs to spatial optimization heuristics that successfully guide them to optimal location solutions. One contention emphasized throughout this paper is that this spatial statistics/optimization interface furnishes another vehicle for delivering spatial statistical benefits to society, which, in turn, benefits spatial statistics by providing better integration of it into novel interdisciplinary contexts.

Spatial sampling, data models, spatial scale and ontologies: Interpreting spatial statistics and machine learning applied to satellite optical remote sensing

Abstract: This paper summarizes the development and application of spatial statistical models in satellite optical remote sensing. The paper focuses on the development of a conceptual model that includes the measurement and sampling processes inherent in remote sensing. We organized this paper into five main sections: introducing the basis of remote sensing, including measurement and sampling; spatial variation, including variation through the object-based data model; advances in spatial statistical modelling; machine learning and explainable AI; a hierarchical ontological model of the nature of remotely sensed scenes. The paper finishes with a summary. We conclude that optical remote sensing provides an important source of data and information for the development of spatial statistical techniques that, in turn, serve as powerful tools to obtain important information from the images.

Spherical Poisson point process intensity function modeling and estimation with measure transport

Abstract: Recent years have seen an increased interest in the application of methods and techniques commonly associated with machine learning and artificial intelligence to spatial statistics. Here, in a celebration of the ten-year anniversary of the journal Spatial Statistics, we bring together normalizing flows, commonly used for density function estimation in machine learning, and spherical point processes, a topic of particular interest to the journal’s readership, to present a new approach for modeling non-homogeneous Poisson process intensity functions on the sphere. The central idea of this framework is to build, and estimate, a flexible bijective map that transforms the underlying intensity function of interest on the sphere into a simpler, reference, intensity function, also on the sphere. Map estimation can be done efficiently using automatic differentiation and stochastic gradient descent, and uncertainty quantification can be done straightforwardly via nonparametric bootstrap. We investigate the viability of the proposed method in a simulation study, and illustrate its use in a proof-of-concept study where we model the intensity of cyclone events in the North Pacific Ocean. Our experiments reveal that normalizing flows present a flexible and straightforward way to model intensity functions on spheres, but that their potential to yield a good fit depends on the architecture of the bijective map, which can be difficult to establish in practice.

Decisions, uncertainty and spatial information

Abstract: In this paper we review how the uncertainty in spatial information has been characterized. This includes both continuous predictions of spatial variables, and thematic maps of landcover classes. We contend that much work in this area has failed to engage adequately with the decision processes of the end-user of information, and that the engagement of spatial statisticians is essential to achieve this. We examine generalized measures of uncertainty, and those focussed on particular decision models. We conclude that the latter are likely to be the most fruitful, particularly if they emerge from a formal decision analysis. We outline the principles of value of information theory, and suggest that this represents an ideal framework in which to develop measures of uncertainty which can support both the rational collection of data and the interpretation of the resulting information.

On the importance of thinking locally for statistics and society

Abstract: Over the past two decades increasing focus has been given to local forms of spatial analysis, both in terms of descriptive statistics and spatial modeling. We term this “thinking locally” Fundamental to thinking locally is that a global approach to spatial analysis may not be suitable and that there may be situations where the conditioned relationships we want to measure vary over space. This paper examines the implications of thinking locally not only for modeling spatial processes but also more broadly in terms of our understanding of behavior in space. We begin with a brief survey of local statistical modeling and what might cause relationships to vary spatially and then describe the operation of one type of local modeling framework – that of (Multiscale) Geographically Weighted Regression – to demonstrate the basic concepts inherent in local models and the type of output that is generated by such models. We then examine the implications of a local approach to statistical analysis focussing on the role of local models compared to spatial regression models, diagnostics for local models, and how a local approach relates to issues of spatial scale which have plagued spatial analysis for decades. Attention is then turned to the implications of a local modeling approach to society, commenting on replicability and how local models can be used to measure previously unmeasurable place-based ‘contextual’ effects. We demonstrate the issues raised throughout the paper with an empirical example of house price determinants.

Multiple change point estimation of trends in Covid-19 infections and deaths in India as compared with WHO regions

Abstract: The present study aims at estimating the multiple change points for the time series data of COVID-19 confirmed cases and deaths and trend estimation within the estimated multiple change points (MCP) in India as compared with WHO regions. The data were described using descriptive statistical measures, and for the estimation of change point's E-divisive procedure was employed. Further, the trend within the estimated change points was tested using Sen's slope and Mann Kendal tests. India, along with the African Region, American region, and South East Asia regions experienced a significant surge in the fresh cases up to the 5th Change point. Among the WHO regions, The American region was the worst hit by the pandemic in case of fresh cases and deaths. While the European region experienced an early negative trend of fresh cases during the 3rd and 4th change point, but later the situation reversed by the 5th (7th July 2020) and 6th (6th August 2020) change point. The trend of deaths in India and the South-East Asia Region was similar, and global deaths had a negative trend from the 4th (17th May 2020) Change point onwards. The change points were estimated with prefixed significance level α < 0.002. Infections and deaths were positively significant for India and SEARO region across change points. Infection was significant at every 30 days interval across other WHO regions, and any delay in the infections was due to the interventions. The European region is expected to have a second wave of positive infections during the 5th and 6th change points though the early two change points were negatively significant. The study highlights the efficacy of change point analysis in understanding the dynamics of covid-19 cases in India and across the world. It further helps to develop effective public health strategies.

Estimation of COVID-19 mortality in the United States using Spatio-temporal Conway Maxwell Poisson model

Abstract: Spatio-temporal Poisson models are commonly used for disease mapping. However, after incorporating the spatial and temporal variation, the data do not necessarily have equal mean and variance, suggesting either over- or under-dispersion. In this paper, we propose the Spatio-temporal Conway Maxwell Poisson model. The advantage of Conway Maxwell Poisson distribution is its ability to handle both under- and over-dispersion through controlling one special parameter in the distribution, which makes it more flexible than Poisson distribution. We consider data from the pandemic caused by the SARS-CoV-2 virus in 2019 (COVID-19) that has threatened people all over the world. Understanding the spatio-temporal pattern of the disease is of great importance. We apply a spatio-temporal Conway Maxwell Poisson model to data on the COVID-19 deaths and find that this model achieves better performance than commonly used spatio-temporal Poisson model.

Adaptive smoothing to identify spatial structure in global lake ecological processes using satellite remote sensing data

Abstract: Satellite remote sensing data are important to the study of environment problems at a global scale. The GloboLakes project aimed to use satellite remote sensing data to investigate the response of the major lakes on Earth to environmental conditions and change. The main challenge to statistical modelling is the identification of the spatial structure in global lake ecological processes from a large number of time series subject to incomplete data and varying uncertainty. This paper introduces a comprehensive modelling procedure, combining adaptive smoothing and functional data analysis, to estimate the smooth curves representing the trend and seasonal patterns in the time series and to cluster the curves over space. Two approaches, based on an irregular basis and an adaptive penalty matrix, are developed to account for the varying uncertainty induced by missing observations and specific constraints (e.g. substantive periods of measurement values of zero in winter). In particular, the adaptive penalty matrix applies a heavier penalty to smooth curve estimates where there is higher uncertainty to prevent over-fitting the noisy/biased data. The modelling procedure was applied to the lake surface water temperature (LSWT) time series from 732 largest lakes globally and the lake chlorophyll-a time series from 535 largest lakes globally. The procedure enabled the identification of nine global lake thermal regions based on the temporal dynamics of LSWT, and the extraction of eight global lake clusters based on the interannual variation in chlorophyll-a and ten clusters to differentiate the seasonal signals.

Bayesian negative binomial regression with spatially varying dispersion: Modeling COVID-19 incidence in Georgia

Abstract: Overdispersed count data arise commonly in disease mapping and infectious disease studies. Typically, the level of overdispersion is assumed to be constant over time and space. In some applications, however, this assumption is violated, and in such cases, it is necessary to model the dispersion as a function of time and space in order to obtain valid inferences. Motivated by a study examining spatiotemporal patterns in COVID-19 incidence, we develop a Bayesian negative binomial model that accounts for heterogeneity in both the incidence rate and degree of overdispersion. To fully capture the heterogeneity in the data, we introduce region-level covariates, smooth temporal effects, and spatially correlated random effects in both the mean and dispersion components of the model. The random effects are assigned bivariate intrinsic conditionally autoregressive priors that promote spatial smoothing and permit the model components to borrow information, which is appealing when the mean and dispersion are spatially correlated. Through simulation studies, we show that ignoring heterogeneity in the dispersion can lead to biased and imprecise estimates. For estimation, we adopt a Bayesian approach that combines full-conditional Gibbs sampling and Metropolis-Hastings steps. We apply the model to a study of COVID-19 incidence in the state of Georgia, USA from March 15 to December 31, 2020.