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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.
Hierarchical Bayesian Sparse Image Reconstruction With Application to MRFM
"... Abstract—This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seam ..."
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Abstract—This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument. Index Terms—Bayesian inference, deconvolution, Markov chain Monte Carlo (MCMC) methods, magnetic resonance force microscopy
Fortune or Virtue: TimeVariant Volatilities Versus Parameter Drifting in U.S. Data ∗
, 2010
"... participants at several seminars for useful comments, and Béla Személy for invaluable research assistance. Beyond the usual disclaimer, we must note that any views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta, the Federal Reserve Bank of ..."
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Cited by 30 (7 self)
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participants at several seminars for useful comments, and Béla Személy for invaluable research assistance. Beyond the usual disclaimer, we must note that any views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta, the Federal Reserve Bank of Philadelphia, or the Federal Reserve System. Finally, we also thank the NSF for financial support.
Testing Nonnested Models of International Relations: Reevaluating Realism
, 2001
"... Unknown to most world politics scholars and political scientists in general, traditional methods of model discrimination such as likelihood ratio tests, Ftests, and artificial nesting fail when applied to nonnested models. That the vast majority of models used throughout international relations ..."
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Cited by 27 (6 self)
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Unknown to most world politics scholars and political scientists in general, traditional methods of model discrimination such as likelihood ratio tests, Ftests, and artificial nesting fail when applied to nonnested models. That the vast majority of models used throughout international relations research have nonlinear functional forms complicates the problem. The purpose of this research is to suggest methods of properly discriminating between nonnested models and then to demonstrate how these techniques can shed light on substantive debates in international relations. Reanalysis of two wellknown articles that compare structural realism to various alternatives suggests that the evidence against realism in both articles is overstated.
2004. “Comparing Dynamic Equilibrium Economies to Data: A Bayesian Approach
 Journal of Econometrics
"... of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors ’ responsibility. ..."
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Cited by 24 (0 self)
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of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors ’ responsibility.
Bayesian Multiple Comparisons Using Dirichlet Process Priors
 Journal of the American Statistical Association
, 1996
"... We consider the problem of multiple comparisons from a Bayesian viewpoint. The family of Dirichlet process priors is applied in the form of baseline prior/likelihood combinations, to obtain posterior probabilities for various hypotheses. The baseline prior/likelihood combinations considered here are ..."
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Cited by 23 (0 self)
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We consider the problem of multiple comparisons from a Bayesian viewpoint. The family of Dirichlet process priors is applied in the form of baseline prior/likelihood combinations, to obtain posterior probabilities for various hypotheses. The baseline prior/likelihood combinations considered here are beta/binomial, normal/inverted gamma with equal variances and a hierarchical nonconjugate normal/inverted gamma prior on treatment means. The prior probabilities of the hypotheses depend directly on the concentration parameter of the Dirichlet process prior. The problem is analytically intractable; we use Gibbs sampling. The posterior probabilities of the hypotheses are easily obtained as a byproduct in evaluating the marginal posterior distributions of the parameters. The proposed procedure is compared with Duncan's multiple range test and shown to be more powerful under certain alternative hypotheses. Keywords: Gibbs sampling, beta/binomial prior, normal/inverted gamma prior, hierarchica...
Bayesian Regression Analysis With Scale Mixtures of Normals
, 1999
"... This paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of Normals. Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and scale parameters. ..."
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Cited by 21 (7 self)
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This paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of Normals. Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and scale parameters. We find that whereas existence of the posterior distribution does not depend on the choice of the design matrix or the mixing distribution, both of them can crucially intervene in the existence of posterior moments. We identify some useful characteristics that allow for an easy verification of the existence of a wide range of moments. In addition, we provide full characterizations under sampling from finite mixtures of Normals, Pearson VII or certain Modulated Normal distributions. For empirical applications, a numerical implementation based on the Gibbs sampler is recommended.
A tutorial introduction to decision theory
 IEEE Transactions on Systems Science and Cybernetics
, 1968
"... AbstractDecision theory provides a rational framework for choosing between alternative courses of action when the consequences resulting from this choice are imperfectly known. Two ..."
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Cited by 20 (0 self)
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AbstractDecision theory provides a rational framework for choosing between alternative courses of action when the consequences resulting from this choice are imperfectly known. Two
Approximate Bayesian Inference for Quantiles
"... Suppose data consist of a random sample from a distribution function FY, which is unknown, and that interest focuses on inferences on θ, a vector of quantiles of FY. When the likelihood function is not fully specified, a posterior density cannot be calculated and Bayesian inference is difficult. Th ..."
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Cited by 20 (1 self)
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Suppose data consist of a random sample from a distribution function FY, which is unknown, and that interest focuses on inferences on θ, a vector of quantiles of FY. When the likelihood function is not fully specified, a posterior density cannot be calculated and Bayesian inference is difficult. This article considers an approach which relies on a substitution likelihood characterized by a vector of quantiles. Properties of the substitution likelihood are investigated, strategies for prior elicitation are presented, and a general framework is proposed for quantile regression modeling. Posterior computation proceeds via a Metropolis algorithm that utilizes a normal approximation to the posterior. Results from a simulation study are presented, and the methods are illustrated through application to data from a genotoxicity experiment.