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.
Papers published on a yearly basis
Papers
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TL;DR: An approximate ML estimator that is computed simultaneously with a maximum a posteriori (MAP) image estimate and the results of a Monte Carlo study that examines the bias and variance of this estimator when applied to image restoration are presented.
Abstract: The parameters of the prior, the hyperparameters, play an important role in Bayesian image estimation. Of particular importance for the case of Gibbs priors is the global hyperparameter, /spl beta/, which multiplies the Hamiltonian. Here we consider maximum likelihood (ML) estimation of /spl beta/ from incomplete data, i.e., problems in which the image, which is drawn from a Gibbs prior, is observed indirectly through some degradation or blurring process. Important applications include image restoration and image reconstruction from projections. Exact ML estimation of /spl beta/ from incomplete data is intractable for most image processing. Here we present an approximate ML estimator that is computed simultaneously with a maximum a posteriori (MAP) image estimate. The algorithm is based on a mean field approximation technique through which multidimensional Gibbs distributions are approximated by a separable function equal to a product of one-dimensional (1-D) densities. We show how this approach can be used to simplify the ML estimation problem. We also show how the Gibbs-Bogoliubov-Feynman (GBF) bound can be used to optimize the approximation for a restricted class of problems. We present the results of a Monte Carlo study that examines the bias and variance of this estimator when applied to image restoration.
142 citations
TL;DR: The relative pose and motion of cooperative satellites using on-board sensors is solved by using only visual sensors, which measurements are processed through robust filtering algorithms and it is shown that, even in the noncooperative case, there is information that can be extracted pertaining to the relative attitude and target structure.
Abstract: Estimating the relative pose and motion of cooperative satellites using on-board sensors is a challenging problem. When the satellites are noncooperative, the problem becomes even more complicated, as there might be poor a priori information about the motion and structure of the target satellite. In this paper, the mentioned problem is solved by using only visual sensors, which measurements are processed through robust filtering algorithms. Using two cameras mounted on a chaser satellite, the relative state with respect to a target satellite, including the position, attitude, and rotational and translational velocities, is estimated. The new approach employs a stereoscopic vision system for tracking a set of feature points on the target spacecraft. The perspective projection of these points on the two cameras constitutes the observation model of an iterated extended Kalman filter (IEKF) estimation scheme. Using new theoretical results, the information contained in the visual data is quantified using the Fisher information matrix. It is shown that, even in the noncooperative case, there is information that can be extracted pertaining to the relative attitude and target structure. Finally, a method is proposed for rendering the relative motion filtering algorithm robust to uncertainties in the target's inertia tensor. This is accomplished by endowing the IEKF with a maximum a posteriori identification scheme for determining the most probable inertia tensor from several available hypotheses. The performance of the new filtering algorithm is validated by Monte-Carlo simulations. Also a preliminary experimental evaluation is provided.
140 citations
TL;DR: Advantages and disadvantages of joint maximum likelihood, marginal maximum likelihood and Bayesian methods of parameter estimation in item response theory are discussed and compared in this article, where the authors compare the advantages and disadvantages for different methods.
Abstract: Advantages and disadvantages of joint maximum likelihood, marginal maximum likelihood, and Bayesian methods of parameter estimation in item response theory are discussed and compared.
140 citations
TL;DR: A novel data reduction method which requires no inter-sensor collaboration and results in only a subset of the sensor measurements transmitted to the FC, and performs competitively with alternative methods, under different sensing conditions, while having lower computational complexity.
Abstract: Consider a wireless sensor network (WSN) with a fusion center (FC) deployed to estimate signal parameters from noisy sensor measurements. If the WSN has a large number of low-cost, battery-operated sensor nodes with limited transmission bandwidth, then conservation of transmission resources (power and bandwidth) is paramount. To this end, the present paper develops a novel data reduction method which requires no inter-sensor collaboration and results in only a subset of the sensor measurements transmitted to the FC. Using interval censoring as a data-reduction method, each sensor decides separately whether to censor its acquired measurements based on a rule that promotes censoring of measurements with least impact on the estimator mean-square error (MSE). Leveraging the statistical distribution of sensor data, the censoring mechanism and the received uncensored data, FC-based estimators are derived for both deterministic (via maximum likelihood estimation) and random parameters (via maximum a posteriori probability estimation) for a linear-Gaussian model. Quantization of the uncensored measurements at the sensor nodes offers an additional degree of freedom in the resource conservation versus estimator MSE reduction tradeoff. Cramer-Rao bound analysis for the different censor-estimators and censor-quantizer estimators is also provided to benchmark and facilitate MSE-based performance comparisons. Numerical simulations corroborate the analytical findings and demonstrate that the proposed censoring-estimation approach performs competitively with alternative methods, under different sensing conditions, while having lower computational complexity.
140 citations
TL;DR: In this paper, the role of martingale limit theory in the theory of maximum likelihood estimation for continuous-time stochastic processes is investigated and analogues of classical statistical concepts and quantities are also suggested.
Abstract: This paper is mainly concerned with the asymptotic theory of maximum likelihood estimation for continuous-time stochastic processes. The role of martingale limit theory in this theory is developed. Some analogues of classical statistical concepts and quantities are also suggested. Various examples that illustrate parts of the theory are worked through, producing new results in some cases. The role of diffusion approximations in estimation is also explored. MAXIMUM LIKELIHOOD ESTIMATION; CONTINUOUS-TIME STOCHASTIC PROCESSES; ASYMPTOTIC THEORY; MARTINGALE LIMIT THEORY; DIFFUSION APPROXIMATIONS
139 citations