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Articles 1 - 24 of 24
Full-Text Articles in Physical Sciences and Mathematics
Letter To The Editor, Noel A. Cressie
Spatial Statistics In The Presence Of Location Error With An Application To Remote Sensing Of The Environment, Noel A. Cressie, John Kornak
Spatial Statistics In The Presence Of Location Error With An Application To Remote Sensing Of The Environment, Noel A. Cressie, John Kornak
Professor Noel Cressie
Techniques for the analysis of spatial data have, to date, tended to ignore any effect caused by error in specifying the spatial locations at which measurements are recorded. This paper reviews the methods for adjusting spatial inference in the presence of data-location error, particularly for data that. have a continuous spatial index (geostatistical data). New kriging equations are developed and evaluated based on a simulation experiment. They are also applied to remote-sensing data from the Total Ozone Mapping Spectrometer instrument on the Nimbus-7 satellite, where the location error is caused by assignment of the data to their nearest grid-cell centers. …
Small-Area Estimation: An Appraisal - Comment, Noel A. Cressie, Mark S. Kaiser
Small-Area Estimation: An Appraisal - Comment, Noel A. Cressie, Mark S. Kaiser
Professor Noel Cressie
Malay Ghosh and Jon Rao have presented us with a well written exposition of the topic of small area estimation. The past literature has been de-cidedly influenced by linear modeling, and we see that clearly in their paper. There has also been a tendency to judge the performance of the estimation methods by concentrating on a single, arbitrary small area. In our comment, we shall discuss what opportunities there might be to expand the class of statistical models for small area data and to consider multivariate aspects of small area estimation.
Plenary: Nonparametric Hypothesis Testing For A Spatial Signal, Noel A. Cressie
Plenary: Nonparametric Hypothesis Testing For A Spatial Signal, Noel A. Cressie
Professor Noel Cressie
Summary form only given. Nonparametric hypothesis testing for a spatial signal can involve a large number of hypotheses. For instance, two satellite images of the same scene, taken before and after an event, could be used to test a hypothesis that the event has no environmental impact. This is equivalent to testing that the mean difference of "after-before" is zero at each of the (typically thousands of) pixels that make up the scene. In such a situation, conventional testing procedures that control the overall Type I error deteriorate as the number of hypotheses increase. Powerful testing procedures are needed for …
The Vprt - A Sequential Testing Procedure Dominating The Sprt, Noel A. Cressie, Peter Morgan
The Vprt - A Sequential Testing Procedure Dominating The Sprt, Noel A. Cressie, Peter Morgan
Professor Noel Cressie
Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed …
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 …
A Spatial Analysis Of Variance Applied To Soil-Water Infiltration, C Gotway, Noel A. Cressie
A Spatial Analysis Of Variance Applied To Soil-Water Infiltration, C Gotway, Noel A. Cressie
Professor Noel Cressie
A spatial analysis of variance uses the spatial dependence among the observations to modify the usual interference procedures associated with a statistical linear model. When spatial correlation is present, the usual tests for presence of treatment effects may no longer be valid, and erroneous conclusions may result from assuming that the usual F ratios are F distributed. This is demonstrated using a spatial analysis of soil-water infiltration data. Emphasis is placed on modeling the spatial dependence structure with geostatistical techniques, and this spatial dependence structure is then used to test hypotheses about fixed effects using a nested linear model. -Authors
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 …
Bayesian Hierarchical Analysis Of Minefield Data, Noel A. Cressie, Andrew B. Lawson
Bayesian Hierarchical Analysis Of Minefield Data, Noel A. Cressie, Andrew B. Lawson
Professor Noel Cressie
Based on remote sensing of a potential minefield, point locations are identified, some of which may not be mines. The mines and mine-like objects are to be distinguished based on their point patterns, although it must be emphasized that all we see is the superposition of their locations. In this paper, we construct a hierarchical spatial point-process model that accounts for the different patterns of mines and mine-like objects and uses posterior analysis to distinguish between them. Our Bayesian approach is applied to COBRA image data obtained from the NSWC Coastal Systems Station, Dahlgren Division, Panama City, Florida. 2003 Copyright …
Fast, Resolution-Consistent Spatial Prediction Of Global Processes From Satellite Data, Hsin-Cheng Huang, Noel A. Cressie, John Gabrosek
Fast, Resolution-Consistent Spatial Prediction Of Global Processes From Satellite Data, Hsin-Cheng Huang, Noel A. Cressie, John Gabrosek
Professor Noel Cressie
Polar orbiting satellites remotely sense the earth and its atmosphere, producing datasets that give daily global coverage. For any given day, the data are many and measured at spatially irregular locations. Our goal in this article is to predict values that are spatially regular at different resolutions; such values are often used as input to general circulation models (GCMs) and the like. Not only do we wish to predict optimally, but because data acquisition is relentless, our algorithm must also process the data very rapidly. This article applies a multiresolution autoregressive tree-structured model, and presents a new statistical prediction methodology …
Random Set Theory And Problems Of Modeling, Noel A. Cressie, G M. Laslett
Random Set Theory And Problems Of Modeling, Noel A. Cressie, G M. Laslett
Professor Noel Cressie
The three- or four-dimensional world in which we live is full of objects to be measured and summarized. Very often a parsimonious finite collection of measurements is enough for scientific investigation into an object’s genesis and evolution. There is a growing need, however, to describe and model objects through their form as well as their size. The purpose of this article is to show the potentials and limitations of a probabilistic and statistical approach. Collections of objects (the data) are assimilated to a random set (the model), whose parameters provide description and/or explanation.
Data Mining Of Misr Aerosol Product Using Spatial Statistics, Tao Shi, Noel A. Cressie
Data Mining Of Misr Aerosol Product Using Spatial Statistics, Tao Shi, Noel A. Cressie
Professor Noel Cressie
In climate models, aerosol forcing is the major source of uncertainty in climate forcing, over the industrial period. To reduce this uncertainty, instruments on satellites have been put in place to collect global data. However, missing and noisy observations impose considerable difficulties for scientists researching global aerosol distribution, aerosol transportation, and comparisons between satellite observations and global-climate-model outputs. In this paper, we propose a Spatial Mixed Effects (SME) statistical model to predict the missing values, denoise the observed values, and quantify the spatial-prediction uncertainties. The computations associated with the SME model are linear scalable to the number of data points, …
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 …
Some Diagnostics For Markov Random Fields, Noel A. Cressie, Prasenjit Kapat
Some Diagnostics For Markov Random Fields, Noel A. Cressie, Prasenjit Kapat
Professor Noel Cressie
The development of diagnostics to check the fit of a proposed Markov random field (MRP) to data is a very important problem in spatial statistics. In this article, the consequences of fitting a given MRF to spatial data are visualized using diagnostic plots. The Gaussian MRF known as the conditional autoregressive model is featured. Various types of departures of the data from the fitted MRF model are calculated, allowing locally influential observations to be highlighted using the MRF-Neighborhoods plot. Through a global summary statistic and the Model-Comparison plot, we compare MRF models that differ both in terms of the neighborhood …
Long-Lead Prediction Of Pacific Ssts Via Bayesian Dynamic Modeling, L M. Berliner, Christopher K. Wikle, Noel A. Cressie
Long-Lead Prediction Of Pacific Ssts Via Bayesian Dynamic Modeling, L M. Berliner, Christopher K. Wikle, Noel A. Cressie
Professor Noel Cressie
Tropical Pacific sea surface temperatures (SSTs) and the accompanying El Nino-Southern Oscillation phenomenon are recognized as significant components of climate behavior. The atmospheric and oceanic processes involved display highly complicated variability over both space and time. Researchers have applied both physically derived modeling and statistical approaches to develop long-lead predictions of tropical Pacific SSTs. The comparative successes of these two approaches are a subject of substantial inquiry and some controversy. Presented in this article is a new procedure for long-lead forecasting of tropical Pacific SST fields that expresses qualitative aspects of scientific paradigms for SST dynamics in a statistical manner. …
Asymptotic Inference For Spatial Cdfs Over Time, Jun Zhu, S N. Lahiri, Noel A. Cressie
Asymptotic Inference For Spatial Cdfs Over Time, Jun Zhu, S N. Lahiri, Noel A. Cressie
Professor Noel Cressie
A spatial cumulative distribution function (SCDF) is a random function that provides a statistical summary of a random process over a spatial domain of interest. In this paper, we consider a spatio-temporal process and establish statistical methodology to analyze changes in the SCDF over time. We develop hypothesis testing to detect a difference in the spatial random processes at two time points, and we construct a prediction interval to quantify such discrepancy in the corresponding SCDFs. Using a spatial subsampling method, we show that our inferences are valid asymptotically. As an illustration, we apply these inference procedures to test and …
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.
A Spatial-Temporal Statistical Approach To Command And Control Problems In Battle-Space Digitization, David A. Wendt, Noel A. Cressie, Gardar Johannesson
A Spatial-Temporal Statistical Approach To Command And Control Problems In Battle-Space Digitization, David A. Wendt, Noel A. Cressie, Gardar Johannesson
Professor Noel Cressie
There are considerable difficulties in the integration, visualization, and overall management of battle-space information for the purpose of Command and Control (C2). One problem that we see as being important is the timely combination of digital information from multiple (possibly disparate) sources in a dynamically evolving environment. That is, there is a need to assimilate incoming data rapidly, so as to provide the battle commander with up-to-date knowledge about the battle-space and thereby to facilitate the command-decision process. In this paper, we present a spatial-temporal approach to obtaining accurate estimates of the constantly changing battlefield, based on noisy data from …
A Robust-Resistant Spatial Analysis Of Soil Water Infiltration., Noel A. Cressie, R Horton
A Robust-Resistant Spatial Analysis Of Soil Water Infiltration., Noel A. Cressie, R Horton
Professor Noel Cressie
Concentrates on estimating the spatial correlations between soil water infiltration observations, with special emphasis on resistant methods to remove nonstationarity. After this removal, robust semivariogram estimators are used to examine the spatial dependencies for various tillage treatments. There is some indication that infiltration characteristics inherit different types of spatial dependency, depending on the tillage treatment applied.-from Authors
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 …