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.

A Bayesian classification approach with application to speech recognition

Abstract: A Bayesian approach to classification of parametric information sources whose statistics are not explicitly given is studied and applied to recognition of speech signals based upon Markov modeling. A classifier based on generalized likelihood ratios, which depends only on the available training and testing data, is developed and shown to be optimal in the sense of achieving the highest asymptotic exponential rate of decay of the error probability. The proposed approach is compared to the standard classification approach used in speech recognition, in which the parameters for the sources are first estimated from the given training data, and then the maximum a posteriori decision rule is applied using the estimated statistics. >

MAP Visibility Estimation for Large-Scale Dynamic 3D Reconstruction

Abstract: Many traditional challenges in reconstructing 3D motion, such as matching across wide baselines and handling occlusion, reduce in significance as the number of unique viewpoints increases. However, to obtain this benefit, a new challenge arises: estimating precisely which cameras observe which points at each instant in time. We present a maximum a posteriori (MAP) estimate of the time-varying visibility of the target points to reconstruct the 3D motion of an event from a large number of cameras. Our algorithm takes, as input, camera poses and image sequences, and outputs the time-varying set of the cameras in which a target patch is visibile and its reconstructed trajectory. We model visibility estimation as a MAP estimate by incorporating various cues including photometric consistency, motion consistency, and geometric consistency, in conjunction with a prior that rewards consistent visibilities in proximal cameras. An optimal estimate of visibility is obtained by finding the minimum cut of a capacitated graph over cameras. We demonstrate that our method estimates visibility with greater accuracy, and increases tracking performance producing longer trajectories, at more locations, and at higher accuracies than methods that ignore visibility or use photometric consistency alone.

A weighted strategy to handle likelihood uncertainty in Bayesian inference

Abstract: The sensitivity of posterior inferences to model specification can be considered as an indicator of the presence of outliers, that are to be considered as highly unlikely values under the assumed model. The occurrence of anomalous values can seriously alter the shape of the likelihood function and lead to posterior distributions far from those one would obtain without these data inadequacies. In order to deal with these hindrances, a robust approach is discussed, which allows us to obtain outliers' resistant posterior distributions with properties similar to those of a proper posterior distribution. The methodology is based on the replacement of the genuine likelihood by a weighted likelihood function in the Bayes' formula.

Reconstruction From Aperture-Filtered Samples With Application to Scatterometer Image Reconstruction

Abstract: This paper approaches scatterometer image reconstruction as the inversion of a discrete noisy aperture-filtered sampling operation. Aperture-filtered sampling is presented and contrasted with conventional and irregular sampling. Discrete reconstruction from noise-free aperture-filtered samples is investigated and contrasted with conventional continuous reconstruction approaches. The discrete approach enables analytical treatment of the reconstruction grid resolution and the effective resolution imposed by the sampling and reconstruction operations. The noisy case is also explored. A reconstruction estimator based on maximum a posteriori (MAP) estimation is proposed to recover the conventional samples from noisy scatterometer measurements. This approach enables the scatterometer noise distribution to be appropriately accounted for in the reconstruction operation. The MAP and conventional reconstruction approaches are applied to the SeaWinds scatterometer and the Advanced Wind Scatterometer, and the effective resolution of the different methods is analyzed. The MAP approach produces results consistent with the well-established scatterometer image reconstruction (SIR) algorithm. The MAP approach significantly enhances the resolution at the expense of increased noise. Although a detailed noise-versus-resolution tradeoff analysis is beyond the scope of this paper, the new framework allows for a more general treatment than the ad hoc tuning parameters of the SIR algorithm.