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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Texture Analysis Using Partially Ordered Markov Models, Jennifer Davidson, Ashit Talukder, Noel A. Cressie
Texture Analysis Using Partially Ordered Markov Models, Jennifer Davidson, Ashit Talukder, Noel A. Cressie
Professor Noel Cressie
Texture is a phenomenon in image data that continues to receive wide-spread interest due to its broad range of applications. The paper focuses on but one of several ways to model textures, namely, the class of stochastic texture models. the authors introduce a new spatial stochastic model called partially ordered Markov models, or POMMs. They show how POMMs are a generalization of a class of models called Markov mesh models, or MMMs, that allow an explicit closed form of the joint probability, just as do MMMs. While POMMs are a type of Markov random field model (MRF), the general MRFs …
Spatial Mixture Models Based On Exponential Family Conditional Distributions, M Kaiser, Noel A. Cressie, J Lee
Spatial Mixture Models Based On Exponential Family Conditional Distributions, M Kaiser, Noel A. Cressie, J Lee
Professor Noel Cressie
Spatial statistical models are applied in many problems for which dependence in observed random variables is not easily explained by a direct scientific mechanism. In such situations there may be a latent spatial process that acts to produce the observed spatial pattern. Scientific interest often centers on the latent process and the degree of spatial dependence that characterizes it. Such latent processes may be thought of as spatial mixing distributions. We present methods for the specification of flexible joint distributions to model spatial processes through multi-parameter exponential family conditional distributions. One approach to the analysis of these models is Monte …
Models And Inference For Clustering Of Locations Of Mines And Minelike Objects, Noel A. Cressie, Andrew B. Lawson
Models And Inference For Clustering Of Locations Of Mines And Minelike Objects, Noel A. Cressie, Andrew B. Lawson
Professor Noel Cressie
Mines and mine-like objects are distributed throughout an area of interest. Remote sensing of the area form an aircraft yields image data that represent the superposition of electromagnetic emissions from the mines and mine-like objects. In this article we build a hierarchical statistical model for the reconstruction of mien locations given a point pattern of the superposition of mines and mine-like objects. It is shown how inference on the mine locations can be obtained using Markov chain Monte Carlo methods.
A Spatial Analysis Of Multivariate Output From Regional Climate Models, Stephan Sain, Reinhard Furrer, Noel A. Cressie
A Spatial Analysis Of Multivariate Output From Regional Climate Models, Stephan Sain, Reinhard Furrer, Noel A. Cressie
Professor Noel Cressie
Climate models have become an important tool in the study of climate and climate change, and ensemble experiments consisting of multiple climate-model runs are used in studying and quantifying the uncertainty in climate-model output. However, there are often only a limited number of model runs available for a particular experiment, and one of the statistical challenges is to characterize the distribution of the model output. To that end, we have developed a multivariate hierarchical approach, at the heart of which is a new representation of a multivariate Markov random field. This approach allows for flexible modeling of the multivariate spatial …
Size And Power Considerations For Testing Loglinear Models Using Divergence Test Statistics, Noel A. Cressie, L Pardo, M Del Carmen Pardo
Size And Power Considerations For Testing Loglinear Models Using Divergence Test Statistics, Noel A. Cressie, L Pardo, M Del Carmen Pardo
Professor Noel Cressie
In this article, we assume that categorical data are distributed according to a multinomial distribution whose probabilities follow a loglinear model. The inference problem we consider is that of hypothesis testing in a loglinear-model setting. The null hypothesis is a composite hypothesis nested within the alternative. Test statistics are chosen from the general class of divergence statistics. This article collects together the operating characteristics of the hypothesis test based on both asymptotic (using large-sample theory) and finite-sample (using a designed simulation study) results. Members of the class of power divergence statistics are compared, and it is found that the Cressie-Read …
Mine Boundary Detection Using Partially Ordered Markov Models, Xia Hua, Jennifer Davidson, Noel A. Cressie
Mine Boundary Detection Using Partially Ordered Markov Models, Xia Hua, Jennifer Davidson, Noel A. Cressie
Professor Noel Cressie
Detection of objects in images in an automated fashion is necessary for many applications, including automated target recognition. In this paper, we present results of an automated boundary detection procedure using a new subclass of Markov random fields (MRFs), called partially ordered Markov models (POMMs). POMMs offer computational advantages over general MRFs. We show how a POMM can model the boundaries in an image. Our algorithm for boundary detection uses a Bayesian approach to build a posterior boundary model that locates edges of objects having a closed loop boundary. We apply our method to images of mines with very good …
Minimum Phi Divergence Estimator And Hierarchical Testing In Loglinear Models, Noel A. Cressie, Leandro Pardo
Minimum Phi Divergence Estimator And Hierarchical Testing In Loglinear Models, Noel A. Cressie, Leandro Pardo
Professor Noel Cressie
In this paper we consider inference based on very general divergence measures, under assumptions of multinomial sampling and loglinear models. We define the minimum phi divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. This estimator is then used in a phi divergence goodness-of-fit statistic, which is the basis of two new statistics for solving the problem of testing a nested sequence of loglinear models.
Asymptotic Properties Of Maximum (Composite) Likelihood Estimators For Partially Ordered Markov Models, Hsin-Cheng Huang, Noel A. Cressie
Asymptotic Properties Of Maximum (Composite) Likelihood Estimators For Partially Ordered Markov Models, Hsin-Cheng Huang, Noel A. Cressie
Professor Noel Cressie
Partially ordered Markov models (POMMs) are Markov random fields (MRFs) with neighborhood structures derivable from an associated partially ordered set. The most attractive feature of POMMs is that their joint distributions can be written in closed and product form. Therefore, simulation and maximum likelihood estimation for the models is quite straightforward, which is not the case in general for MRF models. In practice, one often has to modify the likelihood to account for edge components; the resulting composite likelihood for POMMs is similarly straightforward to maximize. In this article, we use a martingale approach to derive the asymptotic properties of …
Flexible Spatial Models For Kriging And Cokriging Using Moving Averages And The Fast Fourier Transform (Fft), Jay M. Ver Hoef, Noel A. Cressie, Ronald P. Barry
Flexible Spatial Models For Kriging And Cokriging Using Moving Averages And The Fast Fourier Transform (Fft), Jay M. Ver Hoef, Noel A. Cressie, Ronald P. Barry
Professor Noel Cressie
Models for spatial autocorrelation and cross-correlation depend on the distance and direction separating two locations, and are constrained so that for all possible sets of locations, the covariance matrices implied from the models remain nonnegative-definite. Based on spatial correlation, optimal linear predictors can be constructed that yield complete maps of spatial fields from incomplete and noisy spatial data. This methodology is called kriging if the data are of only one variable type, and it is called cokriging if it is of two or more variable types. Historically, to satisfy the nonnegative-definite condition, cokriging has used coregionalization models for cross-variograms, even …