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Objective Bayesian Analysis of Spatially Correlated Data
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2000
"... Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly specified to be of a certain form (e.g., spherical, power exponential, rational quadratic, or Matérn) wi ..."
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Cited by 52 (7 self)
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Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly specified to be of a certain form (e.g., spherical, power exponential, rational quadratic, or Matérn) with a small number of unknown parameters. We consider objective Bayesian analysis of such spatial models, when the mean function of the Gaussian random field is specified as in a linear model. It is thus necessary to determine an objective (or default) prior distribution for the unknown mean and covariance parameters of the random field. We first
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.
Space and SpaceTime Modeling Using Process Convolutions
"... . A continuous spatial model can be constructed by convolving a very simple, perhaps independent, process with a kernel or point spread function. This approach for constructing a spatial process o#ers a number of advantages over specification through a spatial covariogram. In particular, this proces ..."
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Cited by 39 (4 self)
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. A continuous spatial model can be constructed by convolving a very simple, perhaps independent, process with a kernel or point spread function. This approach for constructing a spatial process o#ers a number of advantages over specification through a spatial covariogram. In particular, this process convolution specification leads to compuational simplifications and easily extends beyond simple stationary models. This paper uses process convolution models to build space and spacetime models that are flexible and able to accomodate large amounts of data. Data from environmental monitoring is considered. 1 Introduction Modeling spatial data with Gaussian processes is the common thread of all geostatistical analyses. Some notable references in this area include Matheron (1963), Journel and Huijbregts (1978), Ripley (1981), Cressie (1991), Wackernagel (1995), and Stein (1999). A common approach is to model spatial dependence through the covariogram c(), so that covariance between any t...
On the Change of Support Problem for SpatioTemporal Data
, 2000
"... lis, MN, 55455. The work of the first author was supported in part by NSF grant DMS 9971206; that of the first and second authors was supported in part by NSF/EPA grant SES 9978238; and that of the second and third authors was supported in part by National Institute of Environmental Health Sciences ..."
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Cited by 18 (1 self)
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lis, MN, 55455. The work of the first author was supported in part by NSF grant DMS 9971206; that of the first and second authors was supported in part by NSF/EPA grant SES 9978238; and that of the second and third authors was supported in part by National Institute of Environmental Health Sciences (NIEHS) Grant 1R01ES07750. The authors are grateful to Profs. Paige Tolbert and James Mulholland for providing and permitting analysis of the Atlanta ozone dataset. 1 Key words: Bayesian methods; Environmental risk analysis; Geographic Information System (GIS); Kriging; Modifiable areal unit problem; Simulationbased model fitting. 1 Introduction Consider a univariate variable that is spatially observed. In particular, assume that it is observed either at points in space, which we refer to as pointreferenced or simply point data, or over areal units (e.g., counties or zip codes), which we refer to as bloc
Frailty modeling for spatially correlated survival data, with application to infant mortality in Minnesota
, 2003
"... this paper, we consider random effects corresponding to clusters that are spatially arranged, such as clinical sites or geographical regions. That is, we might suspect that random effects corresponding to strata in closer proximity to each other might also be similar in magnitude. Such spatial arran ..."
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Cited by 14 (5 self)
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this paper, we consider random effects corresponding to clusters that are spatially arranged, such as clinical sites or geographical regions. That is, we might suspect that random effects corresponding to strata in closer proximity to each other might also be similar in magnitude. Such spatial arrangement of the strata can be modeled in several ways, but we group these ways into two general settings: geostatistical approaches, where we use the exact geographic locations (e.g. latitude and longitude) of the strata, and lattice approaches, where we use only the positions of the strata relative to each other (e.g. which counties neighbor which others). We compare our approaches in the context of a dataset on infant mortality in Minnesota counties between 1992 and 1996. Our main substantive goal here is to explain the pattern of infant mortality using important covariates (sex, race, birth weight, age of mother, etc.) while accounting for possible (spatially correlated) differences in hazard among the counties. We use the GIS ArcView to map resulting fitted hazard rates, to help search for possible lingering spatial correlation. The DIC criterion (Spiegelhalter et al.,Journal of the Royal Statistical Society, Series B 2002, to appear) is used to choose among various competing models. We investigate the quality of fit of our chosen model, and compare its results when used to investigate neonatal versus postneonatal mortality. We also compare use of our timetoevent outcome survival model with the simpler dichotomous outcome logistic model. Finally, we summarize our findings and suggest directions for future research
Bayesian Modeling and Inference for Geometrically Anisotropic Spatial Data
 Mathematical Geology
, 1999
"... A geometrically anisotropic spatial process can be viewed as being a linear transformation of an isotropic spatial process. Customary semivariogram estimation techniques often involve ad hoc selection of the linear transformation to reduce the region to isotropy and then fitting a valid parametric s ..."
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Cited by 11 (3 self)
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A geometrically anisotropic spatial process can be viewed as being a linear transformation of an isotropic spatial process. Customary semivariogram estimation techniques often involve ad hoc selection of the linear transformation to reduce the region to isotropy and then fitting a valid parametric semivariogram to the data under the transformed coordinates. We propose a Bayesian methodology which simultaneously estimates the linear transformation and the other semivariogram parameters. In addition, the Bayesian paradigm allows full inference for any characteristic of the geometrically anisotropic model rather than merely providing a point estimate. Our work is motivated by a data set of scallop catches in the Atlantic Ocean in 1990 and also in 1993. The 1990 data provide useful prior information about the nature of the anisotropy of the process. Exploratory data analysis (EDA) techniques such as directional empirical semivariograms and the rose diagram are widely used by practitioners....
On Geodetic Distance Computations in Spatial Modelling
 Biometrics
, 2004
"... Statisticians analyzing spatial data often need to detect and model associations based upon distances on the earth's surface. Accurate computation of distances are sought for exploratory and interpretation purposes, as well as for developing numerically stable estimation algorithms. When the data co ..."
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Cited by 10 (0 self)
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Statisticians analyzing spatial data often need to detect and model associations based upon distances on the earth's surface. Accurate computation of distances are sought for exploratory and interpretation purposes, as well as for developing numerically stable estimation algorithms. When the data come from locations on the spherical earth, application of Euclidean or planar metrics for computing distances is not straightforward. Yet, planar metrics are desirable because of their easier interpretability, easy availability in software packages and wellestablished theoretical properties. While distance computations are indispensable in spatial modelling, their importance and impact upon statistical estimation and prediction have gone largely unaddressed. This article explores the di#erent options in using planar metrics and investigates their impact upon spatial modelling.
Spatial Modeling and Prediction under Range Anisotropy
, 1999
"... For modeling spatial processes, we propose rich classes of range anisotropic covariance structures that greatly increase the scope of variogram contours in R² and include geometric anisotropy and isotropy as special cases. We demonstrate how the class of all completely monotonic isotropic vario ..."
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Cited by 3 (3 self)
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For modeling spatial processes, we propose rich classes of range anisotropic covariance structures that greatly increase the scope of variogram contours in R² and include geometric anisotropy and isotropy as special cases. We demonstrate how the class of all completely monotonic isotropic variograms can be extended to capture range anisotropy and illustrate with two examples, the Matérn and the general exponential. We adopt a Bayesian perspective and fit these range anisotropic covariance models using samplingbased methods. In the presence of measurement error/microscale effect, we develop the noiseless predictive distribution. We analyze a data set of scallop catches, withholding ten sites, to compare the accuracy and precision of the standard and noiseless predictive distributions.
Bayesian Hot Spot Detection in the Presence of a Spatial Trend: Application to Total Nitrogen Concentration in the Chesapeake Bay
, 1999
"... In the Chesapeake Bay, a decreasing gradient of total nitrogen concentrations extends from the highest values in the north at the mouth of the Susquehanna River to the lowest values in the south near the Atlantic Ocean. We illustrate an attractive modeling technique for these data with right skewed ..."
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Cited by 3 (1 self)
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In the Chesapeake Bay, a decreasing gradient of total nitrogen concentrations extends from the highest values in the north at the mouth of the Susquehanna River to the lowest values in the south near the Atlantic Ocean. We illustrate an attractive modeling technique for these data with right skewed sampling distributions by coupling the BoxCox family of power transformations with a spatial trend in a random eld model. We extend the Bayesian Transformed Gaussian (BTG) model proposed by De Oliveira, Kedem and Short (1997, Journal of the American Statistical Association 92, 14221433) to the case where the data contain measurement error and propose an eÆcient Monte Carlo algorithm to t the model. The median function is employed as the measure of spatial trend, which for the BTG model oers advantages over the customarily used mean function. We develop a methodology for making inference about hot spots that is appealing in the presence of geographic covariates (i.e., a spatial trend). ...
Prediction, Interpolation and Regression for Spatially Misaligned Data
 Sankhya
, 2002
"... SUMMARY. Spatial models for pointreferenced data are used for capturing spatial association and for providing spatial prediction, typically in the presence of explanatory variables. The goal of this paper is to treat the situation where there is misalignment between at least one of the explanatory ..."
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Cited by 3 (0 self)
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SUMMARY. Spatial models for pointreferenced data are used for capturing spatial association and for providing spatial prediction, typically in the presence of explanatory variables. The goal of this paper is to treat the situation where there is misalignment between at least one of the explanatory variables and the response variable. In this context we formalize three inference problems. One, which we call interpolation, seeks to infer about missing response at an observed explanatory location. The second, which we call prediction, seeks to infer about a response at a location with the explanatory variable unobserved. The last, which we call regression, seeks to investigate the functional relationship between the response and explanatory variable through the conditional mean of the response. We treat both the case of Gaussian and binary spatial response. We adopt a Bayesian approach, providing full posterior inference for each of the above problems. We illustrate both cases using portions of a study of isopod burrows in the Negev desert in Israel. 1.