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Process Modeling for Space-Time ExtremesAlan E. GelfandDep’t of Statistical Science, Duke University, EUAIncreasingly, data are being gathered to investigate the behavior of extremes of a process over spaceand time. By now, there is a considerable literature addressing this problem. This talk will focus onmodeling for such a setting. In particular, there are several paths that can be taken to formulate suchstochastic specifications. We can model the process directly and study the induced behavior for extremes.Though, perhaps attractive, this is very computationally demanding. We can model the sampled extremesdirectly, drawing upon the elegant characterizations of max-stable processes that have appearedin the literature. This approach runs into computational challenges as well, though recent work usingcomposite likelihood ideas is promising. We can model the data in a hierarchical fashion, introducinga latent process model. Now, we have at our disposal rich and easily interpretable specifications andhave access to familiar MCMC model-fitting machinery. After some review and discussion of the firsttwo possibilities, we focus on the last, illuminating the range of modeling that is available and the computationalissues. Recent work by Sang and Gelfand will provide the basis for this as well as examples.Finally, some new extensions using Dirichlet Process mixing will be proposed. This is joint work withHuiyan Sang.15
Product Partition Models with Correlated ParametersRosangela H. LoschiDepartamento de Estatística, Universidade Federal de Minas GeraisIn time series, Bayesian partition models aim at partitioning the entire observation period into disjointtemporal clusters. Each cluster is an aggregation of sequential observations and a simple model is adoptedwithin each cluster. The main inferential problem is the estimation of the number and locations of thetemporal clusters. The popularity of partition models is justified by its flexibility to analyze changepoint or clustering problems. However, its original formulation assumes a common parameter indexingthe distributions of the observations into the same temporal cluster. Furthermore, it also assumesindependence among the common parameters associated with different temporal clusters. This approachmay lead to an inaccurate identification of the number of clusters.We extend the well-known product partition model (PPM) for clustering analysis in the temporalcontext. We also assume independence among parameters in different temporal clusters, but contraryto what is assumed in the PPM, we consider that the observations in the same cluster have their distributionsindexed by different parameters. Although different, the parameters are similar for observationswithin a given cluster. This is done by adopting a Gibbs distribution as the prior specification for thecanonical parameters. As a result, the parameters within the same temporal cluster are correlated. Oneimportant advantage in allowing similar parameters within a temporal cluster is that, rather than havingan unknown dimension, the dimension of the parameter vector is fixed and equal to the time serieslength. This facilitates the numerical procedures used to obtain the posterior distribution.We carried out several simulations and real dataset analyzes showing that our model provides betterestimates for all parameters, including the number and position of the temporal clusters, even forsituations favoring the PPM.This is joint work with Renato M. Assunção and João V. D. Monteiro.16
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Page 9 and 10: Particle LearningCarlos M. Carvalho
Page 12 and 13: Uso de Métodos Bayesianos em Anál
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Accounting for Latent Spatio-Tempor
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Uma Abordagem Bayesiana para Proces
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A Bayesian Analysis for the General
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Comparação de um Modelo Dinâmico
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Estimando Variações de Temperatur
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A Bayesian Approach to Multivariate
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Bayesian Inference for Gamma Modula
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Computational Tools for Comparing A
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Modelo Partição Produto com “Cl
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BIC Criterion for Minimal Markov Mo
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Estimadores Lineares Bayesianos em
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Modelos de Volatilidade Estocástic
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Processo de Difusão Multivariado c
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Generalized Latent Factor Models fo
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Measuring Vulnerability via Spatial
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Medidas do Valor Preditivo de um Mo
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Aproximações Analíticas para Pos
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Modelo de Risco Logístico Dependen
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A Practical Approach to Elicit Mult
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Modelos Dinâmicos para Deformaçã
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A Semiparametric Bayesian Approach
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Modelo Weibull Modificado de Longa
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Abordagem Bayesiana para Modelos GA
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Modelo Bayesiano Geral de Classe La
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Métodos de Estimação em Modelos
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LASSO Bayesiano no Mapeamento de QT
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Estudo das Matrizes de Covariância
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Sensibilidade da Inferência Bayesi
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Análise Bayesiana para o Estudo de
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Uma Abordagem Bayesiana para Modelo
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Construção de Tábuas de Mortalid
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Um Procedimento Bayesiano para a An
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Um Novo Modelo para Dependência Es
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Distribuição Geométrica Exponenc
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Morbidade Pulmonar e Condições Cl
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Standard Setting for a Rasch Poisso
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Modelo Logístico Misto com Classes
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Metodologia Bayesiana para Detecç
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Modelos Espaço-Temporais para Dado
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Comparação de Modelos para a Iden
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Modelos Multivariados de Regressão
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Estimação Bayesiana em Modelos de
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Previsão de Resultados de Jogos de
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Uma Abordagem Bayesiana para Modelo
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Análise Bayesiana do Modelo Log-Bi
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Desempate TécnicoFilipe Jaeger Zab
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10 o Encontro Brasileiro de Estatí
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