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Informationtheoretic asymptotics of Bayes methods
 IEEE Transactions on Information Theory
, 1990
"... AbstractIn the absence of knowledge of the true density function, Bayesian models take the joint density function for a sequence of n random variables to be an average of densities with respect to a prior. We examine the relative entropy distance D,, between the true density and the Bayesian densit ..."
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Cited by 107 (10 self)
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AbstractIn the absence of knowledge of the true density function, Bayesian models take the joint density function for a sequence of n random variables to be an average of densities with respect to a prior. We examine the relative entropy distance D,, between the true density and the Bayesian density and show that the asymptotic distance is (d/2Xlogn)+ c, where d is the dimension of the parameter vector. Therefore, the relative entropy rate D,,/n converges to zero at rate (logn)/n. The constant c, which we explicitly identify, depends only on the prior density function and the Fisher information matrix evaluated at the true parameter value. Consequences are given for density estimation, universal data compression, composite hypothesis testing, and stockmarket portfolio selection. 1.
A Bayesian Approach to Financial Model Calibration, Uncertainty Measures and Optimal Hedging
"... Michaelmas 2009This thesis is dedicated to the late ..."
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Cited by 1 (1 self)
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Michaelmas 2009This thesis is dedicated to the late
Statistical Linear Destriping of SatelliteBased PushbroomType Images
"... Abstract—This paper introduces a new selfcalibration destriping technique for pushbroomtype satellite imaging systems. Selfcalibration means that no specific training data are required. It is based on the statistical estimation of each detector gain from the observed image, assuming a linear respo ..."
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Abstract—This paper introduces a new selfcalibration destriping technique for pushbroomtype satellite imaging systems. Selfcalibration means that no specific training data are required. It is based on the statistical estimation of each detector gain from the observed image, assuming a linear response. Both theoretical and practical behaviors are studied. Our technique is shown to outperform simpler techniques based on column averages in terms of gain estimation precision while keeping the computational cost within admissible limits. Index Terms—Calibration, estimation, gain measurement, image restoration, image sensors, radiometry. Hervé Carfantan, Member, IEEE, and Jérôme Idier © 2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. I.
New Tools for Consistency in Bayesian Nonparametrics
"... Posterior consistency and the parallel behaviour of consistency of maximum likelihood estimators is analyzed in nonparametric statistical problems. The framework is the hypoStrong Law of Large Numbers, a form of “onesided ” Uniform Law of Large Numbers. Keywords: ..."
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Posterior consistency and the parallel behaviour of consistency of maximum likelihood estimators is analyzed in nonparametric statistical problems. The framework is the hypoStrong Law of Large Numbers, a form of “onesided ” Uniform Law of Large Numbers. Keywords:
BAYESIAN FREQUENTIST HYBRID INFERENCE
, 2009
"... Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a set of multiple parameters, which can be divided into two d ..."
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Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a set of multiple parameters, which can be divided into two disjoint subsets. On one set, a frequentist method may be favored and on the other, the Bayesian. This motivates a joint estimation procedure in which some of the parameters are estimated Bayesian, and the rest by the maximumlikelihood estimator in the same parametric model, and thus keep the strengths of both the methods and avoid their weaknesses. Such a hybrid procedure gives us more flexibility in achieving overall inference advantages. We study the consistency and highorder asymptotic behavior of the proposed estimator, and illustrate its application. Also, the results imply a new method for constructing objective prior.
The Canadian Journal of Statistics
"... La revue canadienne de statistique Asymptotic normality of the posterior given a statistic ..."
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La revue canadienne de statistique Asymptotic normality of the posterior given a statistic