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14
The Consistency of Posterior Distributions in Nonparametric Problems
 Ann. Statist
, 1996
"... We give conditions that guarantee that the posterior probability of every Hellinger... ..."
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Cited by 89 (4 self)
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We give conditions that guarantee that the posterior probability of every Hellinger...
Kullback Leibler property of kernel mixture priors in Bayesian density estimation
 Electronic J. Statist
, 2008
"... Positivity of the prior probability of KullbackLeibler neighborhood around the true density, commonly known as the KullbackLeibler property, plays a fundamental role in posterior consistency. A popular prior for Bayesian estimation is given by a Dirichlet mixture, where the kernels are chosen depe ..."
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Cited by 8 (3 self)
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Positivity of the prior probability of KullbackLeibler neighborhood around the true density, commonly known as the KullbackLeibler property, plays a fundamental role in posterior consistency. A popular prior for Bayesian estimation is given by a Dirichlet mixture, where the kernels are chosen depending on the sample space and the class of densities to be estimated. The KullbackLeibler property of the Dirichlet mixture prior has been shown for some special kernels like the normal density or Bernstein polynomial, under appropriate conditions. In this paper, we obtain easily verifiable sufficient conditions, under which a prior obtained by mixing a general kernel possesses the KullbackLeibler property. We study a wide variety of kernel used in practice, including the normal, t, histogram, Weibull densities and so on, and show that the KullbackLeibler property holds if some easily verifiable conditions are satisfied at the true density. This gives a catalog of conditions required for the KullbackLeibler property, which can be readily used in applications. AMS (2000) subject classification. Primary 62G07, 62G20.
The Elimination of Nuisance Parameters
, 2004
"... We review the Bayesian approach to the problem of the elimination of nuisance parameters from a statistical model. Many Bayesian statisticians feel that the framework of Bayesian statistics is so clear and simple that the elimination of nuisance parameters should not be considered a problem: one has ..."
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Cited by 2 (0 self)
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We review the Bayesian approach to the problem of the elimination of nuisance parameters from a statistical model. Many Bayesian statisticians feel that the framework of Bayesian statistics is so clear and simple that the elimination of nuisance parameters should not be considered a problem: one has simply to compute the marginal posterior distribution of the parameter of interest. However we will argue that this exercise need not be so simple from a practical perspective. The paper is divided in two main parts: the first deals with regular parametric models whereas the second will focus on non regular problem, including the socalled Neyman and Scott’s class of models and semiparametric models where the nuisance parameter lies in an infinite dimensional space. Finally we relate the issues of the elimination of nuisance parameters to other, apparently different, problems. Occasionally, we will mention non Bayesian treatment of nuisance parameters, mainly for comparative analyses.
Characterizing the variance improvement in linear Dirichlet random effects models
 Statist. Probab. Lett
, 2009
"... An alternative to the classical mixed model with normal random effects is to use a Dirichlet process to model the random effects. Such models have proven useful in practice, and we have observed a noticeable variance reduction, in the estimation of the fixed effects, when the Dirichlet process is us ..."
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Cited by 1 (1 self)
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An alternative to the classical mixed model with normal random effects is to use a Dirichlet process to model the random effects. Such models have proven useful in practice, and we have observed a noticeable variance reduction, in the estimation of the fixed effects, when the Dirichlet process is used instead of the normal. In this paper we formalize this notion, and give a theoretical justification for the expected variance reduction. We show that for almost all data vectors, the posterior variance from the Dirichlet random effects model is smaller than that from the normal random effects model.
mixture priors in Bayesian density estimation
"... Abstract: Positivity of the prior probability of KullbackLeibler neighborhood around the true density, commonly known as the KullbackLeibler property, plays a fundamental role in posterior consistency. A popular prior for Bayesian estimation is given by a Dirichlet mixture, where the kernels are c ..."
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Abstract: Positivity of the prior probability of KullbackLeibler neighborhood around the true density, commonly known as the KullbackLeibler property, plays a fundamental role in posterior consistency. A popular prior for Bayesian estimation is given by a Dirichlet mixture, where the kernels are chosen depending on the sample space and the class of densities to be estimated. The KullbackLeibler property of the Dirichlet mixture prior has been shown for some special kernels like the normal density or Bernstein polynomial, under appropriate conditions. In this paper, we obtain easily verifiable sufficient conditions, under which a prior obtained by mixing a general kernel possesses the KullbackLeibler property. We study a wide variety of kernel used in practice, including the normal, t, histogram, gamma, Weibull densities and so on, and show that the KullbackLeibler property holds if some easily verifiable conditions are satisfied at the true density. This gives a catalog of conditions required for the KullbackLeibler property, which can be readily used in applications.
Abstract
"... For concurrent I/O operations, atomicity defines the results in the overlapping file regions simultaneously read/written by requesting processes. Atomicity has been well studied at the file system level, such as POSIX standard. In this paper, we investigate the problems arising from the implement ..."
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For concurrent I/O operations, atomicity defines the results in the overlapping file regions simultaneously read/written by requesting processes. Atomicity has been well studied at the file system level, such as POSIX standard. In this paper, we investigate the problems arising from the implementation of MPI atomicity for concurrent overlapping write access and provide a few programming solutions. Since the MPI definition of atomicity differs from the POSIX one, an implementation that simply relies on the POSIX file systems does not guarantee correct MPI semantics. To have a correct implementation of atomic I/O in MPI, we examine the efficiency of three approaches: 1) file locking, 1