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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.


Papers
More filters
Journal ArticleDOI
TL;DR: A novel detector for single-channel long-haul coherent optical communications, termed stochastic digital backpropagation (SDBP), which takes into account noise from the optical amplifiers in addition to handling deterministic linear and nonlinear impairments is proposed.
Abstract: In this paper, we propose a novel detector for single-channel long-haul coherent optical communications, termed stochastic digital backpropagation (SDBP), which takes into account noise from the optical amplifiers in addition to handling deterministic linear and nonlinear impairments. We discuss the design approach behind this detector, which is based on the maximum a posteriori (MAP) principle. As closed-form expressions of the MAP detector are not tractable for coherent optical transmission, we employ the framework of Bayesian graphical models, which allows a numerical evaluation of the proposed detector. Through simulations, we observe that by accounting for nonlinear signal—noise interactions, we achieve a significant improvement in system reach with SDBP over digital backpropagation (DBP) for systems with periodic inline optical dispersion compensation. In uncompensated links with high symbol rates, the performance difference in terms of system reach for SDBP over DBP is small. In the absence of noise, the proposed detector is equivalent to the well-known DBP detector.

69 citations

Journal ArticleDOI
TL;DR: In this article, the authors estimate multicomponent stress strength reliability by assuming the Burr-XII distribution, and the reliability is estimated using the maximum likelihood method of estimation and results are compared using the Monte Carlo simulation for small samples.
Abstract: In this paper, we estimate multicomponent stress-strength reliability by assuming Burr-XII distribution. The research methodology adopted here is to estimate the parameter using maximum likelihood estimation. Reliability is estimated using the maximum likelihood method of estimation and results are compared using the Monte Carlo simulation for small samples. Using real data sets we illustrate the procedure clearly.

69 citations

Proceedings Article
01 Aug 1997
TL;DR: A class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency are described and regions of completeness are identified and preliminary empirical evaluation on randomly generated networks are provided.
Abstract: This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable explanation, belief updating and finding the maximum a posteriori hypothesis. We identify regions of completeness and provide preliminary empirical evaluation on randomly generated networks.

69 citations

Journal ArticleDOI
TL;DR: In this paper, the authors presented a general expression for a lognormal filter given an arbitrary nonlinear galaxy bias and derived this filter as the maximum a posteriori solution for the matter field with a given mean field and modeling the observed galaxy distribution by a Poissonian process.
Abstract: We present a general expression for a lognormal filter given an arbitrary nonlinear galaxy bias. We derive this filter as the maximum a posteriori solution assuming a lognormal prior distribution for the matter field with a given mean field and modeling the observed galaxy distribution by a Poissonian process. We have performed a three-dimensional implementation of this filter with a very efficient Newton-Krylov inversion scheme. Furthermore, we have tested it with a dark matter N-body simulation assuming a unit galaxy bias relation and compared the results with previous density field estimators like the inverse weighting scheme and Wiener filtering. Our results show good agreement with the underlying dark matter field for overdensities even above delta~1000 which exceeds by one order of magnitude the regime in which the lognormal is expected to be valid. The reason is that for our filter the lognormal assumption enters as a prior distribution function, but the maximum a posteriori solution is also conditioned on the data. We find that the lognormal filter is superior to the previous filtering schemes in terms of higher correlation coefficients and smaller Euclidean distances to the underlying matter field. We also show how it is able to recover the positive tail of the matter density field distribution for a unit bias relation down to scales of about >~2 Mpc/h.

69 citations

Journal ArticleDOI
TL;DR: A thorough review of MC methods for the estimation of static parameters in signal processing applications is performed, describing many of the most relevant MCMC and IS algorithms, and their combined use.
Abstract: Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the maximum likelihood (ML) or maximum a posteriori (MAP) estimators, or by performing a multi-dimensional integration, as in the minimum mean squared error (MMSE) estimators. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and the Monte Carlo (MC) methodology is one feasible approach. MC methods proceed by drawing random samples, either from the desired distribution or from a simpler one, and using them to compute consistent estimators. The most important families of MC algorithms are the Markov chain MC (MCMC) and importance sampling (IS). On the one hand, MCMC methods draw samples from a proposal density, building then an ergodic Markov chain whose stationary distribution is the desired distribution by accepting or rejecting those candidate samples as the new state of the chain. On the other hand, IS techniques draw samples from a simple proposal density and then assign them suitable weights that measure their quality in some appropriate way. In this paper, we perform a thorough review of MC methods for the estimation of static parameters in signal processing applications. A historical note on the development of MC schemes is also provided, followed by the basic MC method and a brief description of the rejection sampling (RS) algorithm, as well as three sections describing many of the most relevant MCMC and IS algorithms, and their combined use. Finally, five numerical examples (including the estimation of the parameters of a chaotic system, a localization problem in wireless sensor networks and a spectral analysis application) are provided in order to demonstrate the performance of the described approaches.

69 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202364
2022125
2021211
2020244
2019250
2018236