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: In this article, an objective procedure of evaluation of the prior distribution in a Bayesian model is developed and the classical ignorance prior distribution is newly interpreted as the locally impartial prior distribution.
Abstract: In developing an estimate of the distribution of a future observation it becomes natural and necessary to consider a distribution over the space of parameters. This justifies the use of Bayes procedures in statistical inference. An objective procedure of evaluation of the prior distribution in a Bayesian model is developed and the classical ignorance prior distribution is newly interpreted as the locally impartial prior distribution.
146 citations
TL;DR: New criteria for estimating a clustering, which are based on the posterior expected adjusted Rand index, are proposed and are shown to possess a shrinkage property and outperform Binder's loss in a simulation study and in an application to gene expression data.
Abstract: In this paper we address the problem of obtaining a single clustering estimate bc based on an MCMC sample of clusterings c (1) ;c (2) :::;c (M) from the posterior distribution of a Bayesian cluster model. Methods to derive b when the number of groups K varies between the clusterings are reviewed and discussed. These include the maximum a posteriori (MAP) estimate and methods based on the posterior similarity matrix, a matrix containing the posterior probabilities that the observations i and j are in the same cluster. The posterior similarity matrix is related to a commonly used loss function by Binder (1978). Minimization of the loss is shown to be equivalent to maximizing the Rand index between esti- mated and true clustering. We propose new criteria for estimating a clustering, which are based on the posterior expected adjusted Rand index. The criteria are shown to possess a shrinkage property and outperform Binder's loss in a simulation study and in an application to gene expression data. They also perform favorably compared to other clustering procedures.
145 citations
TL;DR: A class of SR algorithms based on the maximum a posteriori (MAP) framework is proposed, which utilize a new multichannel image prior model, along with the state-of-the-art single channel image prior and observation models.
Abstract: Super-resolution (SR) is the term used to define the process of estimating a high-resolution (HR) image or a set of HR images from a set of low-resolution (LR) observations. In this paper we propose a class of SR algorithms based on the maximum a posteriori (MAP) framework. These algorithms utilize a new multichannel image prior model, along with the state-of-the-art single channel image prior and observation models. A hierarchical (two-level) Gaussian nonstationary version of the multichannel prior is also defined and utilized within the same framework. Numerical experiments comparing the proposed algorithms among themselves and with other algorithms in the literature, demonstrate the advantages of the adopted multichannel approach.
145 citations
TL;DR: A new method for analyzing low- density parity-check codes and low-density generator-matrix codes under bit maximum a posteriori probability (MAP) decoding is introduced, based on a rigorous approach to spin glasses, which allows one to construct lower bounds on the entropy of the transmitted message conditional to the received one.
Abstract: A new method for analyzing low-density parity-check (LDPC) codes and low-density generator-matrix (LDGM) codes under bit maximum a posteriori probability (MAP) decoding is introduced. The method is based on a rigorous approach to spin glasses developed by Francesco Guerra. It allows one to construct lower bounds on the entropy of the transmitted message conditional to the received one. Based on heuristic statistical mechanics calculations, we conjecture such bounds to be tight. The result holds for standard irregular ensembles when used over binary-input output-symmetric (BIOS) channels. The method is first developed for Tanner-graph ensembles with Poisson left-degree distribution. It is then generalized to "multi-Poisson" graphs, and, by a completion procedure, to arbitrary degree distribution
145 citations
TL;DR: In this article, a nonparametric prior on the spectral density is described through Bernstein polynomials, and a pseudoposterior distribution is obtained by updating the prior using the Whittle likelihood.
Abstract: This article describes a Bayesian approach to estimating the spectral density of a stationary time series. A nonparametric prior on the spectral density is described through Bernstein polynomials. Because the actual likelihood is very complicated, a pseudoposterior distribution is obtained by updating the prior using the Whittle likelihood. A Markov chain Monte Carlo algorithm for sampling from this posterior distribution is described that is used for computing the posterior mean, variance, and other statistics. A consistency result is established for this pseudoposterior distribution that holds for a short-memory Gaussian time series and under some conditions on the prior. To prove this asymptotic result, a general consistency theorem of Schwartz is extended for a triangular array of independent, nonidentically distributed observations. This extension is also of independent interest. A simulation study is conducted to compare the proposed method with some existing methods. The method is illustrated with ...
144 citations