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33
Hidden Markov models and disease mapping
 Journal of the American Statistical Association
, 2001
"... We present new methodology to extend Hidden Markov models to the spatial domain, and use this class of models to analyse spatial heterogeneity of count data on a rare phenomenon. This situation occurs commonly in many domains of application, particularly in disease mapping. We assume that the counts ..."
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Cited by 57 (4 self)
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We present new methodology to extend Hidden Markov models to the spatial domain, and use this class of models to analyse spatial heterogeneity of count data on a rare phenomenon. This situation occurs commonly in many domains of application, particularly in disease mapping. We assume that the counts follow a Poisson model at the lowest level of the hierarchy, and introduce a finite mixture model for the Poisson rates at the next level. The novelty lies in the model for allocation to the mixture components, which follows a spatially correlated process, the Potts model, and in treating the number of components of the spatial mixture as unknown. Inference is performed in a Bayesian framework using reversible jump MCMC. The model introduced can be viewed as a Bayesian semiparametric approach to specifying exible spatial distribution in hierarchical models. Performance of the model and comparison with an alternative wellknown Markov random field specification for the Poisson rates are demonstrated on synthetic data sets. We show that our allocation model avoids the problem of oversmoothing in cases where the underlying rates exhibit discontinuities, while giving equally good results in cases of smooth gradientlike or highly autocorrelated rates. The methodology is illustrated on an epidemiological application to data on a rare cancer in France.
Generalized spatial Dirichlet process models
, 2007
"... Many models for the study of pointreferenced data explicitly introduce spatial random effects to capture residual spatial association. These spatial effects are customarily modelled as a zeromean stationary Gaussian process. The spatial Dirichlet process introduced by Gelfand et al. (2005) produces ..."
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Cited by 30 (1 self)
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Many models for the study of pointreferenced data explicitly introduce spatial random effects to capture residual spatial association. These spatial effects are customarily modelled as a zeromean stationary Gaussian process. The spatial Dirichlet process introduced by Gelfand et al. (2005) produces a random spatial process which is neither Gaussian nor stationary. Rather, it varies about a process that is assumed to be stationary and Gaussian. The spatial Dirichlet process arises as a probabilityweighted collection of random surfaces. This can be limiting for modelling and inferential purposes since it insists that a process realization must be one of these surfaces. We introduce a random distribution for the spatial effects that allows different surface selection at different sites. Moreover, we can specify the model so that the marginal distribution of the effect at each site still comes from a Dirichlet process. The development is offered constructively, providing a multivariate extension of the stickbreaking representation of the weights. We then introduce mixing using this generalized spatial Dirichlet process. We illustrate with a simulated dataset of independent replications and note that we can embed the generalized process within a dynamic model specification to eliminate the independence assumption.
Approximating Hidden Gaussian Markov Random Fields
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 2003
"... This paper discusses how to construct approximations to a unimodal hidden Gaussian Markov random field on a graph of dimension n when the likelihood consists of mutually independent data. We demonstrate that a class of nonGaussian approximations can be constructed for a wide range of likelihood ..."
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Cited by 19 (4 self)
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This paper discusses how to construct approximations to a unimodal hidden Gaussian Markov random field on a graph of dimension n when the likelihood consists of mutually independent data. We demonstrate that a class of nonGaussian approximations can be constructed for a wide range of likelihood models. They have the appealing properties that exact samples can be drawn from them, the normalisation constant is computable, and the computational complexity is only O(n 2 ) in the spatial case. The nonGaussian approximations are refined versions of a Gaussian approximation. The latter serves well if the likelihood is nearGaussian, but it is not sufficiently accurate when the likelihood is not nearGaussian or if n is large. The accuracy of our approximations can be tuned by intuitive parameters to near any precision. We apply
The Clustered AGgregation (CAG) technique leveraging spatial and temporal correlations in wireless sensor networks
 ACM Trans. Sens. Netw
, 2007
"... Sensed data in Wireless Sensor Networks (WSN) reflect the spatial and temporal correlations of physical attributes existing intrinsically in the environment. In this article, we present the Clustered AGgregation (CAG) algorithm that forms clusters of nodes sensing similar values within a given thres ..."
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Cited by 16 (0 self)
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Sensed data in Wireless Sensor Networks (WSN) reflect the spatial and temporal correlations of physical attributes existing intrinsically in the environment. In this article, we present the Clustered AGgregation (CAG) algorithm that forms clusters of nodes sensing similar values within a given threshold (spatial correlation), and these clusters remain unchanged as long as the sensor values stay within a threshold over time (temporal correlation). With CAG, only one sensor reading per cluster is transmitted whereas with Tiny AGgregation (TAG) all the nodes in the network transmit the sensor readings. Thus, CAG provides energy efficient and approximate aggregation results with small and often negligible and bounded error. In this article we extend our initial work in CAG in five directions: First, we investigate the effectiveness of CAG that exploits the temporal as well as spatial correlations using both the measured and modeled data. Second, we design CAG for two modes of operation (interactive and streaming) to enable CAG to be used in different environments and for different purposes. Interactive mode provides mechanisms for oneshot queries, whereas the streaming mode provides those for continuous queries. Third, we propose a fixed range clustering method, which makes the performance of our system independent of the magnitude of the sensor readings and the network topology. Fourth,
Spacevarying Regression Models: Specifications And Simulation
 COMPUTATIONAL STATISTICS & DATA ANALYSIS 42 (2003) 513  533
, 2003
"... Spacevarying regression models are generalizations of standard linear model where the regression coefficients areal/fkz to change in space. Thespatial structure is specified by a mul#TE/bhEf extension of pairwise difference priors, thusenablEk incorporation of neighboring structures and easysamplTk ..."
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Cited by 14 (2 self)
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Spacevarying regression models are generalizations of standard linear model where the regression coefficients areal/fkz to change in space. Thespatial structure is specified by a mul#TE/bhEf extension of pairwise difference priors, thusenablEk incorporation of neighboring structures and easysamplTk schemes. Bayesian inference is performed by incorporation of a prior distribution for the hyperparameters. This approachlpro to anuntractabl posterior distribution. Inference is approximated by drawing samplg from the posterior distribution. Different samplen schemes areavailIfI and may be used in an MCMCal/zh#hT/ They basicalk differ in the way theyhandl bldl of regression coefficients. Approaches vary fromsamplkI each lch/###TE/bhhTk vector of coefficients tocomplfI ellfI/bhf of al regression coe#cients by anal#TE/b integration. These schemes are compared in terms of their computation, chain autocorrel ##TE/ andresulzI; inference.Resule areilh#hEf/bf withsimulhhf data andapplE# to a real dataset.Relset prior specifications that can accommodate thespatial structure in different forms are al/ discussed. The paperconclhh; with a few general remarks.
Multivariate mixtures of normals with an unknown number of components
 Statist. Comp
, 2006
"... Multivariate techniques and especially cluster analysis have been commonly used in Archaeometry. Exploratory and modelbased techniques of clustering have been applied in geochemical (continuous) data of archaeological artifacts for provenance studies. Modelbased clustering techniques like classifi ..."
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Cited by 13 (0 self)
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Multivariate techniques and especially cluster analysis have been commonly used in Archaeometry. Exploratory and modelbased techniques of clustering have been applied in geochemical (continuous) data of archaeological artifacts for provenance studies. Modelbased clustering techniques like classification maximumlikelihood and mixture maximum likelihood had been used in a lesser extent in this context and although they seem to be suitable for such data, they either present practical difficultieslike high dimensionality of the data or their performance give no evidence to support that they prevail on the standard methods (Papageorgiou et al., 2001). In this paper standard statistical methods (hierarchical clustering, principal components analysis) and the recently developed one of the multivariate mixture of normals with unknown number of components (see Dellaportas and Papageorgiou, 2005) in the category of the model– based ones, are applied and compared. The data set comprises of chemical compositions in 188 ceramic samples derived from the Aegean islands and surrounding areas.
Bayesian Regression and Classification Using Mixtures of Gaussian Processes
, 2002
"... For a large dataset with groups of repeated measurements, a mixture model of Gaussian process priors is proposed for modelling the heterogeneity among the different replications. A hybrid Markov chain Monte Carlo (MCMC) algorithm is developed for the implementation of the model for regression an ..."
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Cited by 5 (2 self)
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For a large dataset with groups of repeated measurements, a mixture model of Gaussian process priors is proposed for modelling the heterogeneity among the different replications. A hybrid Markov chain Monte Carlo (MCMC) algorithm is developed for the implementation of the model for regression and classification. The regression model and its implementation are illustrated by modelling observed Functional Electrical Stimulation experimental results.
Spatially Correlated Allocation Models for Count Data
, 2000
"... Spatial heterogeneity of count data on a rare phenomenon occurs commonly in many domains of application, in particularly in disease mapping. We present new methodology to analyse such data, based on a hierarchical allocation model. We assume that the counts follow a Poisson model at the lowest le ..."
Abstract

Cited by 5 (0 self)
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Spatial heterogeneity of count data on a rare phenomenon occurs commonly in many domains of application, in particularly in disease mapping. We present new methodology to analyse such data, based on a hierarchical allocation model. We assume that the counts follow a Poisson model at the lowest level of the hierarchy, and introduce a finite mixture model for the Poisson rates at the next level. The novelty lies in the allocation model to the mixture components, which follows a spatially correlated process, the Potts model, and in treating the number of components of the spatial mixture as unknown. Inference is performed in a Bayesian framework using reversible jump MCMC. The model introduced can be viewed as a Bayesian semiparametric approach to specifying flexible spatial distribution in hierarchical models. It could also be used in contexts where the spatial mixture subgroups are themselves of interest, as in health care monitoring. Performance of the model and comparison wi...
The Dirichlet labeling process for clustering functional data
, 2010
"... We consider problems involving functional data where we have a collection of functions, each viewed as a process realization, e.g., a random curve or surface. For a particular process realization, we assume that the observation at a given location can be allocated to separate groups via a random a ..."
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Cited by 4 (3 self)
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We consider problems involving functional data where we have a collection of functions, each viewed as a process realization, e.g., a random curve or surface. For a particular process realization, we assume that the observation at a given location can be allocated to separate groups via a random allocation process, which we name the Dirichlet labeling process. We investigate properties of this process and its use as a prior in a mixture model. We develop exact and approximate representations for the labeling process, analyze the global and local clustering behavior, clarify model identifiability and posterior consistency, and develop efficient inference methods for models using such priors. Performance is demonstrated with synthetic data examples, a publichealth application, and an image segmentation task.