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29
The formal definition of reference priors
 ANN. STATIST
, 2009
"... Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain informationtheoretic sense. Reference priors have been r ..."
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Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain informationtheoretic sense. Reference priors have been rigorously defined in specific contexts and heuristically defined in general, but a rigorous general definition has been lacking. We produce a rigorous general definition here and then show how an explicit expression for the reference prior can be obtained under very weak regularity conditions. The explicit expression can be used to derive new reference priors both analytically and numerically.
DIC in variable selection
 Statistica Neerlandica
, 2005
"... Model comparison is discussed from an information theoretic point of view. In particular the posterior predictive entropy is related to the target yielding DIC and modifications thereof. The adequacy of criteria for posterior predictive model comparison is also investigated depending on the comparis ..."
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Cited by 9 (0 self)
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Model comparison is discussed from an information theoretic point of view. In particular the posterior predictive entropy is related to the target yielding DIC and modifications thereof. The adequacy of criteria for posterior predictive model comparison is also investigated depending on the comparison to be made. In particular variable selection as a special problem of model choice is formalized in different ways according to whether the comparison is a comparison across models or within an encompassing model and whether a joint or conditional sampling scheme is applied. DIC has been devised for comparisons across models. Its use in variable selection and that of other criteria is illustrated for a simulated data set. Key words: posterior predictive entropy, mutual information, model comparison, hypothesis testing Running head: DIC 1
Compatibility of prior specifications across linear models
 Statistical Science
, 2008
"... Abstract. Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the number of models increases; on the other hand numerous ..."
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Cited by 8 (3 self)
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Abstract. Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the number of models increases; on the other hand numerous prior specifications can only exacerbate the wellknown sensitivity to prior assignments, thus producing less dependable conclusions. Within the subjective framework, both difficulties can be counteracted by linking priors across models in order to achieve simplification and compatibility; we discuss links with related objective approaches. Given an encompassing, or full, model together with a prior on its parameter space, we review and summarize a few procedures for deriving priors under a submodel, namely marginalization, conditioning, and Kullback–Leibler projection. These techniques are illustrated and discussed with reference to variable selection in linear models adopting a conventional gprior; comparisons with existing standard approaches are provided. Finally, the relative merits of each procedure are evaluated through simulated and real data sets. Key words and phrases: Bayes factor, compatible prior, conjugate prior, gprior, hypothesis testing, Kullback–Leibler projection, nested model, variable selection.
Model Selection via Predictive Explanatory Power 20
 Helsinki University of Technology, Laboratory of Computational Engineering
, 1998
"... We consider model selection as a decision problem from a predictive perspective. The optimal Bayesian way of handling model uncertainty is to integrate over model space. Model selection can then be seen as point estimation in the model space. We propose a model selection method based on KullbackLei ..."
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Cited by 5 (0 self)
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We consider model selection as a decision problem from a predictive perspective. The optimal Bayesian way of handling model uncertainty is to integrate over model space. Model selection can then be seen as point estimation in the model space. We propose a model selection method based on KullbackLeibler divergence from the predictive distribution of the full model to the predictive distributions of the submodels. The loss of predictive explanatory power is defined as the expectation of this predictive discrepancy. The goal is to find the simplest submodel which has a similar predictive distribution as the full model, that is, the simplest submodel whose loss of explanatory power is acceptable. To compute the expected predictive discrepancy between complex models, for which analytical solutions do not exist, we propose to use predictive distributions obtained via kfold crossvalidation. We compare the performance of the method to posterior probabilities (Bayes factors), deviance information criteria (DIC) and direct maximization of the expected utility via crossvalidation.
Information measures in Perspective
, 2010
"... Informationtheoretic methodologies are increasingly being used in various disciplines. Frequently an information measure is adapted for a problem, yet the perspective of information as the unifying notion is overlooked. We set forth this perspective through presenting informationtheoretic methodol ..."
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Cited by 3 (0 self)
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Informationtheoretic methodologies are increasingly being used in various disciplines. Frequently an information measure is adapted for a problem, yet the perspective of information as the unifying notion is overlooked. We set forth this perspective through presenting informationtheoretic methodologies for a set of problems in probability and statistics. Our focal measures are Shannon entropy and KullbackLeibler information. The background topics for these measures include notions of uncertainty and information, their axiomatic foundation, interpretations, properties, and generalizations. Topics with broad methodological applications include discrepancy between distributions, derivation of probability models, dependence between variables, and Bayesian analysis. More specific methodological topics include model selection, limiting distributions, optimal prior distribution and design of experiment, modeling duration variables, order statistics, data disclosure, and relative importance of predictors. Illustrations range from very basic to highly technical ones that draw attention to subtle points.
Intrinsic estimation
 Bayesian Statistics 7
, 2003
"... In this paper the problem of parametric point estimation is addressed from an objective Bayesian viewpoint. Arguing that pure statistical estimation may be appropriately described as a precise decision problem where the loss function is a measure of the divergence between the assumed model and the e ..."
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In this paper the problem of parametric point estimation is addressed from an objective Bayesian viewpoint. Arguing that pure statistical estimation may be appropriately described as a precise decision problem where the loss function is a measure of the divergence between the assumed model and the estimated model, the informationbased intrinsic discrepancy is proposed as an appropriate loss function. The intrinsic estimator is then defined as that minimizing the expected loss with respect to the reference posterior distribution. The resulting estimators are shown have attractive invariance properties. As demonstrated with illustrative examples, the proposed theory either leads to new, arguably better estimators, or provides a new perspective on wellestablished solutions. Keywords:
An Introduction to Bayesian Reference Analysis
 Inference on the Ratio of Multinomial Parameters.” The Statistician
, 1998
"... ..."
Bayesian Hypothesis Testing in Latent Variable Models
, 2010
"... Hypothesis testing using Bayes factors (BFs) is known to suffer from several problems in the context of latent variable models. The first problem is computational. Another problem is that BFs are not well defined under the improper prior. In this paper, a new Bayesian method, based on decision theo ..."
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Cited by 2 (1 self)
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Hypothesis testing using Bayes factors (BFs) is known to suffer from several problems in the context of latent variable models. The first problem is computational. Another problem is that BFs are not well defined under the improper prior. In this paper, a new Bayesian method, based on decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a byproduct of the Bayesian MCMC output and, hence, easy to compute. It is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss function. The finite sample properties are examined using simulated data. The method is also illustrated in the context of a onefactor asset pricing model and a stochastic volatility model with jumps using real data.
A Summary of
 Findings of the WestCentral Florida Coastal Studies Project. USGC Open File Report
, 2001
"... It is known that most cases of idiopathic torsion dystonia (ITD) are inherited in an autosomal dominant fashion. Despite clarification of the underlying genetic defect, no consistent structural lesion has been identified in ITD, and it is probable that a biochemical disturbance is the basis of the d ..."
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It is known that most cases of idiopathic torsion dystonia (ITD) are inherited in an autosomal dominant fashion. Despite clarification of the underlying genetic defect, no consistent structural lesion has been identified in ITD, and it is probable that a biochemical disturbance is the basis of the disorder. To determine whether there is impaired function of the nigrostriatal dopaminergic terminals in ITD we studied 11 subjects with generalized ITD and a positive family history using [18F]dopa and PET scanning. Of these 11 patients, eight had putamen [18F]dopa uptake within the lower half of the normal range, while three had uptake reduced by>2 SDs below the normal mean. The lowest putamen [18F]dopa influx constants were found in the most disabled patients. As these reductions were mild it is unlikely that abnormalities of the nigrostriatal dopaminergic pathway are the primary determinant of either the nature or the severity of dystonic symptoms. In addition, we studied three presumed carriers of the ITD gene. These subjects all had normal striatal [18F]dopa influx constants suggesting that [18F]dopa PET is unsuitable as a screening tool for ITD.
TargetLanguageDriven Agglomerative PartofSpeech Tag Clustering for Machine Translation ∗
"... This paper presents a method for reducing the set of different tags to be considered by a partofspeech tagger. The method is based on a clustering algorithm performed over the states of a hidden Markov model, which is initially trained by considering information not only from the source language, b ..."
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This paper presents a method for reducing the set of different tags to be considered by a partofspeech tagger. The method is based on a clustering algorithm performed over the states of a hidden Markov model, which is initially trained by considering information not only from the source language, but also from the target language, using a new unsupervised technique which has been recently proposed to obtain taggers involved in machine translation systems. Then, a bottomup agglomerative clustering algorithm groups the states of the hidden Markov model according to a similarity measure based on their transition probabilities; this reduces the complexity by grouping the initial finer tags into coarser ones. The experiments show that partofspeech taggers using the coarser tags have smaller error rates than those using the initial finest tags; moreover, considering unsupervised information from the target language results in better clusters compared to those unsupervisedly built from source language information only. 1