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.

Bootstrap methods using prior information

Abstract: SUMMARY Bayesian analysis is subject to the same kinds of misspecification problems which motivate the robustness and nonparametric literature. We present a method of incorporating prior information which performs well without direct knowledge of the error distribution. This is accomplished by replacing the likelihood in Bayes's formula by a bootstrap estimate of the sampling density of a robust estimator. The flexibility of the method is illustrated by examples, and its performance relative to standard Bayesian techniques is evaluated in a Monte Carlo study.

Bayesian structural inference for hidden processes

Abstract: We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological e-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be e-machines, irrespective of estimated transition probabilities. Properties of e-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Track-before-detect procedures for low pulse repetition frequency surveillance radars

Abstract: In this study, the authors present a dynamic programming (DP)-based tracking-before-detect (DP TBD) procedure with reference to a low pulse repetition frequency (PRF) surveillance radar framework. In order to avoid non-linear transformation and meanwhile exploit the ambiguous Doppler information, which is eliminated in most of the literature, the authors model the target dynamics in the measurement coordinates defined by range and apparent Doppler. The target state evolutions in the range–apparent Doppler domain are considered as a hybrid system with the ambiguous number deemed as mode variable. Ambiguity number (or mode) transitions are modelled as state dependent. The authors present a DP TBD method for joint maximum a posteriori (MAP) estimation of the target trajectory in the range–apparent Doppler maps and the corresponding ambiguity sequence, both assumptions of known and unknown nuisance parameters (target power and noise variance) are considered. The detection and tracking performance of the proposed procedure are investigated under several system settings. The effect of the prior uncertainty of the nuisance parameters on the performance is also studied.

A dynamic programming algorithm for phase estimation and data decoding on random phase channels

Abstract: : The problem of simultaneously estimating phase and decoding data symbols from baseband data is posed. The phase sequence is assumed to be a random sequence on the circle and the symbols are assumed to be equally-likely symbols transmitted over a perfectly equalized channel. A dynamic programming algorithm (Viterbi algorithm) is derived for decoding a maximum a posteriori (MAP) phase-symbol sequence on a finite dimensional phase-symbol trellis. A new and interesting principle of optimality for simultaneously estimating phase and decoding phase-amplitude coded symbols leads to an efficient two step decoding procedure for decoding phase-symbol sequences. Simulation results for binary, 8- ARY PM, and 16-QASK symbol sets transmitted over random walk and sinusoidal jitter channels are presented, and compared with results one may obtain with a decision-directed algorithm, or with the binary Viterbi algorithm introduced by Ungerboeck. When phase fluctuations are severe, and the symbol set is rich (as in 16-QASK), MAP phase-symbol sequence decoding on circles is superior to Underboeck's technique, which in turn is superior to decision-directed techniques.

Adaptive total variation-based spectral deconvolution with the split Bregman method

Abstract: Spectroscopic data often suffer from common problems of band overlap and noise This paper presents a maximum a posteriori (MAP)-based algorithm for the band overlap problem In the MAP framework, the likelihood probability density function (PDF) is constructed with Gaussian noise assumed, and the prior PDF is constructed with adaptive total variation (ATV) regularization The split Bregman iteration algorithm is employed to optimize the ATV spectral deconvolution model and accelerate the speed of the spectral deconvolution The main advantage of this algorithm is that it can obtain peak structure information as well as suppress noise simultaneity Simulated and real spectra experiments manifest that this algorithm can satisfactorily recover the overlap peaks as well as suppress noise and are robust to the regularization parameter