Topic
Maximum a posteriori estimation
About: Maximum a posteriori estimation is a research topic. Over the lifetime, 7486 publications have been published within this topic receiving 222291 citations. The topic is also known as: Maximum a posteriori, MAP & maximum a posteriori probability.
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TL;DR: A Bayesian framework to define flexible coupling models for joint tensor decompositions of multiple datasets, and theoretical bounds on the data fusion performance using the Bayesian Cramér-Rao bound are given.
Abstract: A Bayesian framework is proposed to define flexible coupling models for joint tensor decompositions of multiple datasets. Under this framework, a natural formulation of the data fusion problem is to cast it in terms of a joint maximum a posteriori (MAP) estimator. Data-driven scenarios of joint posterior distributions are provided, including general Gaussian priors and non Gaussian coupling priors. We present and discuss implementation issues of algorithms used to obtain the joint MAP estimator. We also show how this framework can be adapted to tackle the problem of joint decompositions of large datasets. In the case of a conditional Gaussian coupling with a linear transformation, we give theoretical bounds on the data fusion performance using the Bayesian Cramer–Rao bound. Simulations are reported for hybrid coupling models ranging from simple additive Gaussian models to Gamma-type models with positive variables and to the coupling of data sets which are inherently of different size due to different resolution of the measurement devices.
51 citations
TL;DR: In this article, the authors obtained Bayes estimates of the parameters and reliability function of a 3-parameter Weibull distribution and compared posterior standard-deviation estimates with the corresponding asymptotic standard deviation estimates of their maximum likelihood counterparts.
Abstract: The authors obtain Bayes estimates of the parameters and reliability function of a 3-parameter Weibull distribution and compare posterior standard-deviation estimates with the corresponding asymptotic standard-deviation estimates of their maximum likelihood counterparts. Numerical examples are given. >
51 citations
TL;DR: The maximum a posteriori probability (MAP) receiver for orthogonal frequency-division multiplexed signals in a fading channel is derived and a low-complexity, suboptimal receiver is obtained and evaluated.
Abstract: We derive the maximum a posteriori probability (MAP) receiver for orthogonal frequency-division multiplexed signals in a fading channel. As the complexity of the MAP receiver is high, we obtain a low-complexity, suboptimal receiver and evaluate its performance.
51 citations
TL;DR: It is shown that the SGM can be extended to such penalized ML objective functions, allowing for new algorithms leading to maximum a posteriori stable solutions, and various classical penalization-regularization terms are introduced to impose a smoothness property on the solution.
Abstract: We consider the problem of restoring astronomical images acquired with charge coupled device cameras. The astronomical object is first blurred by the point spread function of the instrument-atmosphere set. The resulting convolved image is corrupted by a Poissonian noise due to low light intensity, then, a Gaussian white noise is added during the electronic read-out operation. We show first that the split gradient method (SGM) previously proposed can be used to obtain maximum likelihood (ML) iterative algorithms adapted in such noise combinations. However, when ML algorithms are used for image restoration, whatever the noise process is, instabilities due to noise amplification appear when the iteration number increases. To avoid this drawback and to obtain physically meaningful solutions, we introduce various classical penalization-regularization terms to impose a smoothness property on the solution. We show that the SGM can be extended to such penalized ML objective functions, allowing us to obtain new algorithms leading to maximum a posteriori stable solutions. The proposed algorithms are checked on typical astronomical images and the choice of the penalty function is discussed following the kind of object.
51 citations
TL;DR: In this paper, the authors proposed a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and they apply them to learn function approximations as well as to solve inverse problems based on partial differential equations.
51 citations