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Maximum a posteriori estimation for multivariate Gaussian mixture observations of Markov chains
 IEEE Transactions on Speech and Audio Processing
, 1994
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Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE Trans Image Processing
, 2003
"... Abstract—We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussi ..."
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Cited by 512 (17 self)
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Abstract—We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
Image Denoising using Gaussian Scale Mixtures in the Wavelet Domain
 IEEE Transactions on Image Processing
, 2002
"... We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vecto ..."
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Cited by 46 (3 self)
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We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier.
Bayesian adaptive learning of the parameters of hidden Markov model for speech recognition
 IEEE Trans. on SAP
"... AbstractIn this paper, a theoretical framework for Bayesian adaptive training of the parameters of discrete hidden Markov model (DHMM) and of semicontinuous HMM (SCHMM) with Gaussian mixture state observation densities is presented. In addition to formulating the forwardbackward MAP (maximum a po ..."
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Cited by 34 (8 self)
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AbstractIn this paper, a theoretical framework for Bayesian adaptive training of the parameters of discrete hidden Markov model (DHMM) and of semicontinuous HMM (SCHMM) with Gaussian mixture state observation densities is presented. In addition to formulating the forwardbackward MAP (maximum a posterion’) and the segmental MAP algorithms for estimating the above HMM parameters, a computationally efficient segmental quasiBayes algorithm for estimating the statespecific mixture coefficients in SCHMM is developed. For estimating the parameters of the prior densities, a new empirical Bayes method based on the moment estimates is also proposed. The MAP algorithms and the prior parameter specification are directly applicable to training speaker adaptive HMM’s. Practical issues related to the use of the proposed techniques for HMMbased speaker adaptation are studied. The proposed MAP algorithms are shown to be effective especially in the cases in which the training or adaptation data are limited. I.
On adaptive decision rules and decision parameter adaptation for automatic speech recognition
 Proc. IEEE
, 2000
"... Recent advances in automatic speech recognition are accomplished by designing a plugin maximum a posteriori decision rule such that the forms of the acoustic and language model distributions are specified and the parameters of the assumed distributions are estimated from a collection of speech and ..."
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Cited by 34 (4 self)
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Recent advances in automatic speech recognition are accomplished by designing a plugin maximum a posteriori decision rule such that the forms of the acoustic and language model distributions are specified and the parameters of the assumed distributions are estimated from a collection of speech and language training corpora. Maximumlikelihood point estimation is by far the most prevailing training method. However, due to the problems of unknown speech distributions, sparse training data, high spectral and temporal variabilities in speech, and possible mismatch between training and testing conditions, a dynamic training strategy is needed. To cope with the changing speakers and speaking conditions in real operational conditions for highperformance speech recognition, such paradigms incorporate a small amount of speaker and environment specific adaptation data into the training process. Bayesian adaptive learning is an optimal way to combine
Online adaptive learning of the continuous density hidden Markov model based on approximate recursive Bayes estimate
 IEEE Trans. Speech Audio Processing
, 1997
"... Online adaptive learning of the continuous density hidden Markov model based on approximate recursive ..."
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Cited by 34 (12 self)
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Online adaptive learning of the continuous density hidden Markov model based on approximate recursive
MAP Estimation of Continuous Density HMM: Theory and Applications
 In: Proceedings of DARPA Speech and Natural Language Workshop
, 1992
"... We discuss maximum a posteriori estimation of continuous density hidden Markovmodels(CDHMM).The classical MLE reestimation algorithms, namely the forwardbackward algorithm and the segmental kmeans algorithm, are expanded and reestimation formulas are given for HMM with Gaussian mixture observation ..."
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Cited by 32 (6 self)
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We discuss maximum a posteriori estimation of continuous density hidden Markovmodels(CDHMM).The classical MLE reestimation algorithms, namely the forwardbackward algorithm and the segmental kmeans algorithm, are expanded and reestimation formulas are given for HMM with Gaussian mixture observation densities. Because of its adaptive nature, Bayesian learning serves as a unified approach for the following four speech recognition applications, namely parameter smoothing, speaker adaptation, speaker group modeling and corrective training. New experimental results on all four applications are provided to show the effectiveness of the MAP estimation approach. INTRODUCTION Estimation of hidden Markov model (HMM) is usually obtained by the method of maximum likelihood (ML) [1, 10, 6] assuming that the size of the training data is large enough to provide robust estimates. This paper investigates maximum a posteriori (MAP) estimate of continuous density hidden Markov models (CDHMM). The MAP ...
Predictable returns and asset allocation: Should a skeptical investor time the market
 Journal of Econometrics
, 2009
"... are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. Predictable returns and asset allocation: Should a skeptical inv ..."
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Cited by 27 (0 self)
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are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. Predictable returns and asset allocation: Should a skeptical investor time the market? We investigate optimal portfolio choice for an investor who is skeptical about the degree to which excess returns are predictable. Skepticism is modeled as an informative prior over the R 2 of the predictive regression. We find that the evidence is sufficient to convince even an investor with a highly skeptical prior to vary his portfolio on the basis of the dividendprice ratio and the yield spread. The resulting weights are less volatile and deliver superior outofsample performance as compared to the weights implied by an entirely modelbased Are excess returns predictable, and if so, what does this mean for investors? In classic studies of rational valuation (e.g. Samuelson (1965, 1973), Shiller (1981)), risk premia are constant over time and thus excess returns are unpredictable. 1
GENERAL MAXIMUM LIKELIHOOD EMPIRICAL BAYES ESTIMATION OF NORMAL MEANS
, 908
"... We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with i.i.d. normal errors. We prove that under mild moment conditions on the unknown means, the average mean squared error (MSE) of the GMLEB is within an infinitesimal f ..."
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Cited by 26 (1 self)
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We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with i.i.d. normal errors. We prove that under mild moment conditions on the unknown means, the average mean squared error (MSE) of the GMLEB is within an infinitesimal fraction of the minimum average MSE among all separable estimators which use a single deterministic estimating function on individual observations, provided that the risk is of greater order than (log n) 5 /n. We also prove that the GMLEB is uniformly approximately minimax in regular and weak ℓp balls when the order of the lengthnormalized norm of the unknown means is between (log n) κ1 /n
When did Bayesian inference become “Bayesian"?
 BAYESIAN ANALYSIS
, 2006
"... While Bayes’ theorem has a 250year history, and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective “Bayesian” was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesi ..."
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Cited by 24 (1 self)
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While Bayes’ theorem has a 250year history, and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective “Bayesian” was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesian developments, beginning with Bayes’ posthumously published 1763 paper and continuing up through approximately 1970, including the period of time when “Bayesian” emerged as the label of choice for those who advocated Bayesian methods.