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27
Under the hood: issues in the specification and interpretation of spatial regression models
 Agricultural Economics
, 2002
"... This paper reviews a number of conceptual issues pertaining to the implementation of an explicit “spatial ” perspective in applied econometrics. It provides an overview of the motivation for including spatial effects in regression models, both from a theorydriven as well as from a datadriven persp ..."
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Cited by 44 (1 self)
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This paper reviews a number of conceptual issues pertaining to the implementation of an explicit “spatial ” perspective in applied econometrics. It provides an overview of the motivation for including spatial effects in regression models, both from a theorydriven as well as from a datadriven perspective. Considerable attention is paid to the inferential framework necessary to carry out estimation and testing and the different assumptions, constraints and implications embedded in the various specifications available in the literature. The review combines insights from the traditional spatial econometrics literature as well as from geostatistics, biostatistics and medical image analysis.
Computational Methods for Multiplicative Intensity Models using Weighted Gamma . . .
 PROCESSES: PROPORTIONAL HAZARDS, MARKED POINT PROCESSES AND PANEL COUNT DATA
, 2004
"... We develop computational procedures for a class of Bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures. A key feature of our approach is that explicit expressions for posterior distributions of these models share ..."
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Cited by 16 (4 self)
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We develop computational procedures for a class of Bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures. A key feature of our approach is that explicit expressions for posterior distributions of these models share many common structural features with the posterior distributions of Bayesian hierarchical models using the Dirichlet process. Using this fact, along with an approximation for the weighted gamma process, we show that with some care, one can adapt efficient algorithms used for the Dirichlet process to this setting. We discuss blocked Gibbs sampling procedures and Pólya urn Gibbs samplers. We illustrate our methods with applications to proportional hazard models, Poisson spatial regression models, recurrent events, and panel count data.
A Shared Component Model for Detecting Joint and Selective Clustering of Two Diseases
"... The study of spatial variations in disease rates is a common epidemiological approach used to describe geographical clustering of disease and to generate hypotheses about the possible `causes' which could explain apparent differences in risk. Recent statistical and computational developments have le ..."
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Cited by 15 (0 self)
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The study of spatial variations in disease rates is a common epidemiological approach used to describe geographical clustering of disease and to generate hypotheses about the possible `causes' which could explain apparent differences in risk. Recent statistical and computational developments have led to the use of realistically complex models to account for overdispersion and spatial correlation. However, these developments have focused almost exclusively on spatial modelling of a single disease. Many diseases share common risk factors (smoking being an obvious example) and if similar patterns of geographical variation of related diseases can be identified, this may provide more convincing evidence of real clustering in the underlying risk surface. In this paper, we propose a shared component model for the joint spatial analysis of two diseases. The key idea is to separate the underlying risk surface for each disease into a shared and a diseasespecific component. The various component...
Model evaluation and spatial interpolation by Bayesian combination of observations with outputs from numerical models
 Biometrics
, 2005
"... Summary. Constructing maps of dry deposition pollution levels is vital for air quality management, and presents statistical problems typical of many environmental and spatial applications. Ideally, such maps would be based on a dense network of monitoring stations, but this does not exist. Instead, ..."
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Cited by 14 (5 self)
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Summary. Constructing maps of dry deposition pollution levels is vital for air quality management, and presents statistical problems typical of many environmental and spatial applications. Ideally, such maps would be based on a dense network of monitoring stations, but this does not exist. Instead, there are two main sources of information for dry deposition levels in the United States: one is pollution measurements at a sparse set of about 50 monitoring stations called CASTNet, and the other is the output of the regional scale air quality models, called Models3. A related problem is the evaluation of these numerical models for air quality applications, which is crucial for control strategy selection. We develop formal methods for combining sources of information with different spatial resolutions and for the evaluation of numerical models. We specify a simple model for both the Models3 output and the CASTNet observations in terms of the unobserved ground truth, and we estimate the model in a Bayesian way. This provides improved spatial prediction via the posterior distribution of the ground truth, allows us to validate Models3 via the posterior predictive distribution of the CASTNet observations, and enables us to remove the bias in the Models3 output. We apply our methods to data on SO2 concentrations, and we obtain highresolution SO2 distributions by combining observed data with model output. We also conclude that the numerical models perform worse in areas closer to power plants, where the SO2 values are overestimated by the models.
Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis
 Dept
, 2005
"... Abstract: We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the spa ..."
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Cited by 12 (3 self)
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Abstract: We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process. We develop a flexible nonparametric mixture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior for the mixing distribution. Using posterior simulation methods, we obtain full inference for the intensity function and any other functional of the process that might be of interest. We discuss applications to problems where inference for clustering in the spatial point pattern is of interest. Moreover, we consider applications of the methodology to extreme value analysis problems. We illustrate the modeling approach with three previously published data sets. Two of the data sets are from forestry and consist of locations of trees. The third data set consists of extremes from the Dow Jones index over a period of 1303 days.
Analysis of spatial data using generalized linear mixed models and Langevintype Markov chain Monte Carlo
, 2000
"... Markov chain Monte Carlo methods are useful in connection with inference and prediction for spatial generalized linear mixed models, where the unobserved random effects constitute a spatially correlated Gaussian random field. We point out that socalled Langevintype updates are useful for Metropoli ..."
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Cited by 8 (3 self)
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Markov chain Monte Carlo methods are useful in connection with inference and prediction for spatial generalized linear mixed models, where the unobserved random effects constitute a spatially correlated Gaussian random field. We point out that socalled Langevintype updates are useful for MetropolisHastings simulation of the posterior distribution of the random eects given the data. Furthermore, we discuss the use of improper priors in Bayesian analysis of spatial generalized linear mixed models with particular emphasis on the socalled Poissonlog normal model. For this and certain other models nonparametric estimation of the covariance function of the Gaussian field is also studied. The methods are applied to various data sets including counts of weed plants on a field.
Modeling the Impact of TrafficRelated AirPollution On Childhood Respiratory Illness
 IN CASE STUDIES IN BAYESIAN STATISTICS, VOLUME
, 1999
"... Epidemiological studies of the health effects of outdoor air pollution have suffered from a number of methodological difficulties. These include ..."
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Cited by 5 (2 self)
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Epidemiological studies of the health effects of outdoor air pollution have suffered from a number of methodological difficulties. These include
Combining models of health and exposure data: the SAVIAH study
"... Over the last two decades the rate of respiratory illnesses, particularly in children, has shown an apparent increase in almost all countries in the western world, and in many developing countries (Anderson et al. 1994; Burney 1988; Burney et al. 1990). In view of the inexorable rise in traffic volu ..."
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Cited by 5 (1 self)
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Over the last two decades the rate of respiratory illnesses, particularly in children, has shown an apparent increase in almost all countries in the western world, and in many developing countries (Anderson et al. 1994; Burney 1988; Burney et al. 1990). In view of the inexorable rise in traffic volumes and associated emissions of urban air pollutants, this has intensified the search for possible environmental causes for these conditions, including a putative effect of trafficrelated air pollution. The evidence for a link between respiratory illness and air quality remains equivocal however, due in part to major problems of measuring or estimating exposure. Studies have used a range of markers to quantify the exposure to air pollution: some studies have focused on fine particulates (Schwartz 1993; Dockery et al. 1993; Pope et al. 1995), some have used either measured (Nitta et al. 1993) or mo...
Loglinear residual tests of Moran’ I autocorrelation and their applications to Kentucky Breast Cancer Data. Geographical Analysis
, 2005
"... This article bridges the permutation test of Moran’s I to the residuals of a loglinear model under the asymptotic normality assumption. It provides the versions of Moran’s I based on Pearson residuals (I PR) and deviance residuals (I DR) so that they can be used to test for spatial clustering while ..."
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Cited by 4 (4 self)
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This article bridges the permutation test of Moran’s I to the residuals of a loglinear model under the asymptotic normality assumption. It provides the versions of Moran’s I based on Pearson residuals (I PR) and deviance residuals (I DR) so that they can be used to test for spatial clustering while at the same time account for potential covariates and heterogeneous population sizes. Our simulations showed that both IPR and IDR are effective to account for heterogeneous population sizes. The tests based on IPR and IDR are applied to a set of lograte models for earlystage and latestage breast cancer with socioeconomic and accesstocare data in Kentucky. The results showed that socioeconomic and accesstocare variables can sufficiently explain spatial clustering of earlystage breast carcinomas, but these factors cannot explain that for the late stage. For this reason, we used local spatial association terms and located four latestage breast cancer clusters that could not be explained. The results also confirmed our expectation that a high screening level would be associated with a high incidence rate of earlystage disease, which in turn would reduce latestage incidence rates.
Modeling Disease Incidence Data with Spatial and SpatioTemporal Dirichlet Process Mixtures
, 2007
"... Disease incidence or mortality data are typically available as rates or counts for specified regions, collected over time. We propose Bayesian nonparametric spatial modeling approaches to analyze such data. We develop a hierarchical specification using spatial random effects modeled with a Dirichlet ..."
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Cited by 3 (0 self)
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Disease incidence or mortality data are typically available as rates or counts for specified regions, collected over time. We propose Bayesian nonparametric spatial modeling approaches to analyze such data. We develop a hierarchical specification using spatial random effects modeled with a Dirichlet process prior. The Dirichlet process is centered around a multivariate normal distribution. This latter distribution arises from a logGaussian process model that provides a latent incidence rate surface, followed by block averaging to the areal units determined by the regions in the study. With regard to the resulting posterior predictive inference, the modeling approach is shown to be equivalent to an approach based on block averaging of a spatial Dirichlet process to obtain a prior probability model for the finite dimensional distribution of the spatial random effects. We introduce a dynamic formulation for the spatial random effects to extend the model to spatiotemporal settings. Posterior inference is implemented through Gibbs sampling. We illustrate the methodology with simulated data as well as with a data set on lung cancer incidences for all 88 counties in the state of Ohio over an observation period of 21 years.