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Diagnostic Measures for Model Criticism
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1996
"... ... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear mo ..."
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Cited by 13 (1 self)
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... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear models, and variable selection in regression and outlier detection. We illustrate our approach with two applications.
Nonparametric Bayes applications to biostatistics,” Bayesian Nonparametrics: Principles and Practice
 In
, 2010
"... Biomedical research has clearly evolved at a dramatic rate in the past decade, with improvements in technology leading to a fundamental shift in the way in which data are collected and analyzed. Before this paradigm shift, studies were most commonly designed to be simple and to focus on relationship ..."
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Cited by 10 (0 self)
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Biomedical research has clearly evolved at a dramatic rate in the past decade, with improvements in technology leading to a fundamental shift in the way in which data are collected and analyzed. Before this paradigm shift, studies were most commonly designed to be simple and to focus on relationships among a few variables of primary interest. For example, in
A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeability
 Statist. Prob. Letters
, 1997
"... We consider Bayesian nonparametric inference for continuousvalued partially exchangeable data, when the partition of the observations into groups is unknown. This includes changepoint problems and mixture models. As the prior, we consider a mixture of products of Dirichlet processes. We show that ..."
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Cited by 7 (1 self)
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We consider Bayesian nonparametric inference for continuousvalued partially exchangeable data, when the partition of the observations into groups is unknown. This includes changepoint problems and mixture models. As the prior, we consider a mixture of products of Dirichlet processes. We show that the discreteness of the Dirichlet process can have a large effect on inference (posterior distributions and Bayes factors), leading to conclusions that can be different from those that result from a reasonable parametric model. When the observed data are all distinct, the effect of the prior on the posterior is to favor more evenly balanced partitions, and its effect on Bayes factors is to favor more groups. In a hierarchical model with a Dirichlet process as the secondstage prior, the prior can also have a large effect on inference, but in the opposite direction, towards more unbalanced partitions. (~) 1997 Elsevier Science B.V.
A note on the consistency of Bayes factors for testing point null versus nonparametric alternatives
 Journal of Statistical Planning and Inference
, 2004
"... When testing a point null hypothesis versus an alternative that is vaguely specified, a Bayesian test usually proceeds by putting a nonparametric prior on the alternative and then computing a Bayes factor based on the observations. This paper addresses the question of consistency, that is, whether ..."
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Cited by 6 (0 self)
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When testing a point null hypothesis versus an alternative that is vaguely specified, a Bayesian test usually proceeds by putting a nonparametric prior on the alternative and then computing a Bayes factor based on the observations. This paper addresses the question of consistency, that is, whether the Bayes factor is correctly indicative of the null or the alternative as the sample size increases. We establish several consistency results in the affirmative under fairly general conditions. Consistency of Bayes factors for testing a point null versus a parametric alternative has long been known. The results here can also be viewed as the nonparametric extension of the parametric counterpart. MSC: 62G20; 62C10
Bayesian goodness of fit testing with mixtures of triangular distributions
, 2005
"... ABSTRACT. We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a nonparametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular de ..."
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Cited by 3 (2 self)
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ABSTRACT. We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a nonparametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.
© Institute of Mathematical Statistics, 2004 Nonparametric Bayesian Data Analysis
"... Abstract. We review the current state of nonparametric Bayesian inference. The discussion follows a list of important statistical inference problems, including density estimation, regression, survival analysis, hierarchical models and model validation. For each inference problem we review relevant n ..."
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Abstract. We review the current state of nonparametric Bayesian inference. The discussion follows a list of important statistical inference problems, including density estimation, regression, survival analysis, hierarchical models and model validation. For each inference problem we review relevant nonparametric Bayesian models and approaches including Dirichlet process (DP) models and variations, Pólya trees, wavelet based models, neural network models, spline regression, CART, dependent DP models and model validation with DP and Pólya tree extensions of parametric models. Key words and phrases: Dirichlet process, regression, density estimation, survival analysis, Pólya tree, random probability model (RPM).
Bayesian Assessment of GoodnessofFit against Nonparametric Alternatives
, 2000
"... The classical chisquare test of goodnessoffit compares the hypothesis that data arise from some parametric family of distributions, against the nonparametric alternative that they arise from some other distribution. However, the chisquare test requires continuous data to be grouped into arbitrar ..."
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The classical chisquare test of goodnessoffit compares the hypothesis that data arise from some parametric family of distributions, against the nonparametric alternative that they arise from some other distribution. However, the chisquare test requires continuous data to be grouped into arbitrary categories. Furthermore, as the test is based upon an approximation, it can only be used if there is su#cient data. In practice, these requirements are often wasteful of information and overly restrictive. The authors explore the use of the fractional Bayes factor to obtain a Bayesian alternative to the chisquare test when no specific prior information is available. They consider the extent to which their methodology can handle small data sets and continuous data without arbitrary grouping.
Sequential Monte Carlo Methods for Normalized Random Measure with Independent Increments Mixtures
, 2011
"... Normalized random measures with independent increments are a tractable and wide class of nonparametric prior. Sequential Monte Carlo methods are developed for both conjugate and nonconjugate models. Methods for improving efficiency by including Markov chain Monte Carlo steps without increasing comp ..."
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Normalized random measures with independent increments are a tractable and wide class of nonparametric prior. Sequential Monte Carlo methods are developed for both conjugate and nonconjugate models. Methods for improving efficiency by including Markov chain Monte Carlo steps without increasing computational complexity are discussed. A simulation study is used to compare the efficiency of the different algorithms for density estimation. The methods are further illustrated by application to estimation of the marginal likelihood in a goodnessoffit testing example and clustering of time series using a nonconjugate mixture model.