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Markov Random Field (markov + random_field)

Distribution by Scientific Domains
Mathematics and Statistics71%

Selected Abstracts

Gaussian Markov Random Fields: Theory and Applications

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 3 2007
Peter Congdon
No abstract is available for this article. [source]

Variable smoothing in Bayesian intrinsic autoregressions

ENVIRONMETRICS, Issue 8 2007
Mark J. Brewer
Abstract We introduce an adapted form of the Markov random field (MRF) for Bayesian spatial smoothing with small-area data. This new scheme allows the amount of smoothing to vary in different parts of a map by employing area-specific smoothing parameters, related to the variance of the MRF. We take an empirical Bayes approach, using variance information from a standard MRF analysis to provide prior information for the smoothing parameters of the adapted MRF. The scheme is shown to produce proper posterior distributions for a broad class of models. We test our method on both simulated and real data sets, and for the simulated data sets, the new scheme is found to improve modelling of both slowly-varying levels of smoothness and discontinuities in the response surface. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Space varying coefficient models for small area data

ENVIRONMETRICS, Issue 5 2003
Renato M. Assunção
Abstract Many spatial regression problems using area data require more flexible forms than the usual linear predictor for modelling the dependence of responses on covariates. One direction for doing this is to allow the coefficients to vary as smooth functions of the area's geographical location. After presenting examples from the scientific literature where these spatially varying coefficients are justified, we briefly review some of the available alternatives for this kind of modelling. We concentrate on a Bayesian approach for generalized linear models proposed by the author which uses a Markov random field to model the coefficients' spatial dependency. We show that, for normally distributed data, Gibbs sampling can be used to sample from the posterior and we prove a result showing the equivalence between our model and other usual spatial regression models. We illustrate our approach with a number of rather complex applied problems, showing that the method is computationally feasible and provides useful insights in substantive problems. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Generalized Hierarchical Multivariate CAR Models for Areal Data

BIOMETRICS, Issue 4 2005
Xiaoping Jin
Summary In the fields of medicine and public health, a common application of areal data models is the study of geographical patterns of disease. When we have several measurements recorded at each spatial location (for example, information on p, 2 diseases from the same population groups or regions), we need to consider multivariate areal data models in order to handle the dependence among the multivariate components as well as the spatial dependence between sites. In this article, we propose a flexible new class of generalized multivariate conditionally autoregressive (GMCAR) models for areal data, and show how it enriches the MCAR class. Our approach differs from earlier ones in that it directly specifies the joint distribution for a multivariate Markov random field (MRF) through the specification of simpler conditional and marginal models. This in turn leads to a significant reduction in the computational burden in hierarchical spatial random effect modeling, where posterior summaries are computed using Markov chain Monte Carlo (MCMC). We compare our approach with existing MCAR models in the literature via simulation, using average mean square error (AMSE) and a convenient hierarchical model selection criterion, the deviance information criterion (DIC; Spiegelhalter et al., 2002, Journal of the Royal Statistical Society, Series B64, 583,639). Finally, we offer a real-data application of our proposed GMCAR approach that models lung and esophagus cancer death rates during 1991,1998 in Minnesota counties. [source]

Estimating the snow water equivalent on the Gatineau catchment using hierarchical Bayesian modelling

HYDROLOGICAL PROCESSES, Issue 4 2006
Ousmane Seidou
Abstract One of the most important parameters for spring runoff forecasting is the snow water equivalent on the watershed, often estimated by kriging using in situ measurements, and in some cases by remote sensing. It is known that kriging techniques provide little information on uncertainty, aside from the kriging variance. In this paper, two approaches using Bayesian hierarchical modelling are compared with ordinary kriging; Bayesian hierarchical modelling is a flexible and general statistical approach that uses observations and prior knowledge to make inferences on both unobserved data (snow water equivalent on the watershed where there is no measurements) and on the parameters (influence of the covariables, spatial interactions between the values of the process at various sites). The first approach models snow water equivalent as a Gaussian spatial process, for which the mean varies in space, and the other uses the theory of Markov random fields. Although kriging and the Bayesian models give similar point estimates, the latter provide more information on the distribution of the snow water equivalent. Furthermore, kriging may considerably underestimate interpolation error. Copyright © 2006 Environment Canada. Published by John Wiley & Sons, Ltd. [source]

Parameter estimation in Bayesian reconstruction of SPECT images: An aid in nuclear medicine diagnosis

INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2004
Antonio López
Abstract Despite the adequacy of Bayesian methods to reconstruct nuclear medicine SPECT (single-photon emission computed tomography) images, they are rarely used in everyday medical practice. This is primarily because of their computational cost and the need to appropriately select the prior model hyperparameters. We propose a simple procedure for the estimation of these hyperparameters and the reconstruction of the original image and test the procedure on both synthetic and real SPECT images. The experimental results demonstrate that the proposed hyperparameter estimation method produces satisfactory reconstructions. Although we have used generalized Gaussian Markov random fields (GGMRF) as prior models, the proposed estimation method can be applied to any priors with convex potential and tractable partition function with respect to the scale hyperparameter. © 2004 Wiley Periodicals, Inc. Int J Imaging Syst Technol 14, 21,27, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20003 [source]

Hierarchical and Joint Site-Edge Methods for Medicare Hospice Service Region Boundary Analysis

BIOMETRICS, Issue 2 2010
Haijun Ma
Summary Hospice service offers a convenient and ethically preferable health-care option for terminally ill patients. However, this option is unavailable to patients in remote areas not served by any hospice system. In this article, we seek to determine the service areas of two particular cancer hospice systems in northeastern Minnesota based only on death counts abstracted from Medicare billing records. The problem is one of spatial boundary analysis, a field that appears statistically underdeveloped for irregular areal (lattice) data, even though most publicly available human health data are of this type. In this article, we suggest a variety of hierarchical models for areal boundary analysis that hierarchically or jointly parameterize,both,the areas and the edge segments. This leads to conceptually appealing solutions for our data that remain computationally feasible. While our approaches parallel similar developments in statistical image restoration using Markov random fields, important differences arise due to the irregular nature of our lattices, the sparseness and high variability of our data, the existence of important covariate information, and most importantly, our desire for full posterior inference on the boundary. Our results successfully delineate service areas for our two Minnesota hospice systems that sometimes conflict with the hospices' self-reported service areas. We also obtain boundaries for the spatial residuals from our fits, separating regions that differ for reasons yet unaccounted for by our model. [source]