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Showing papers on "Maximum a posteriori estimation published in 1984"


Journal ArticleDOI
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Abstract: We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.

18,761 citations


Journal ArticleDOI
TL;DR: The effect of signal-location uncertainty on the detectability of simple visual signals in uncorrelated image noise is measured and is consistent with the view that humans can act as suboptimal maximum a posteriori probability observers.
Abstract: We have measured the effect of signal-location uncertainty on the detectability of simple visual signals in uncorrelated image noise. An M-alternative forced-choice signal-location identification technique was used with values of M ranging from 2 to 1800. We find high statistical efficiency (50% for aperiodic signals), and results from one value of M can be used to predict all others. The results are consistent with the view that humans can act as suboptimal maximum a posteriori probability observers.

166 citations


Journal ArticleDOI
TL;DR: In this article, a maximum likelihood procedure for the estimation of the parameters of the mover-stayer model is presented and a recursive method of computation of maximum likelihood estimators that is very simple to implement.
Abstract: The discrete time mover-stayer model, a special mixture of two independent Markov chains, has been widely used in modeling the dynamics of social processes. The problem of maximum likelihood estimation of its parameters from the data, however, which consist of a sample of independent realizations of this process, has not been considered in the literature. I present a maximum likelihood procedure for the estimation of the parameters of the mover-stayer model and develop a recursive method of computation of maximum likelihood estimators that is very simple to implement. I also verify that obtained maximum likelihood estimators are strongly consistent. I show that the two estimators of the parameters of the mover-stayer model previously proposed in the literature are special cases of the maximum likelihood estimator derived in this article, that is, they coincide with the maximum likelihood estimator under special conditions. I thus explain the interconnection between existing estimators. I also pre...

112 citations


Journal ArticleDOI
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 of the three 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

47 citations


Journal ArticleDOI
TL;DR: The use of maximum a posteriori probability techniques to estimate the mean values of features used in statistical pattern classification problems, when these mean feature values from the various decision classes are jointly Gaussian random vectors that are correlated across the decision classes.
Abstract: This paper describes the use of maximum a posteriori probability (MAP) techniques to estimate the mean values of features used in statistical pattern classification problems, when these mean feature values from the various decision classes are jointly Gaussian random vectors that are correlated across the decision classes. A set of mathematical formalisms is proposed and used to derive closed-form expressions for the estimates of the class-conditional mean vectors, and for the covariance matrix of the errors of these estimates. Finally, the performance of these algorithms is described for the simple case of a two-class one-feature pattern recognition problem, and compared to the performance of classical estimators that do not exploit the class-to-class correlations of the features' mean values.

39 citations


Journal ArticleDOI
TL;DR: The relationship between Stein estimation of a multivariate normal mean and Bayesian analysis is considered in this article, where the necessity to involve prior information is discussed, and various methods of so doing are reviewed These include direct Bayesian analyses, ad hoc utilization of prior information, restricted class Bayesian and Γ-minimax analyses, and Type II maximum likelihood (empirical Bayes) methods.

26 citations


Journal ArticleDOI
TL;DR: The use of bayesian techniques for image restoration under conditions of partial coherence in both CTEM and STEM is investigated and the effect of coherence and noise on the object restorability is assessed.
Abstract: The use of bayesian techniques for image restoration under conditions of partial coherence in both CTEM and STEM is investigated. Amplitude or phase objects are considered, assuming only a single intensity measurement. The weak-phase approximation is not used. An iterative algorithm for determining the maximum a posteriori probability restored image is determined by using the steepest ascent method. The effect of coherence and noise on the object restorability is assessed.

5 citations


Journal ArticleDOI
TL;DR: In this article, sufficient conditions for cn-consistency of Bayesian and maximum likelihood estimators both in terms of variation distance and in so-called "predictable" terms are given.
Abstract: Sulficient conditions are given for cn-consistency of Bayesian and maximum likelihood estimators both in terms of variation distance and in so-called “predictable” terms.

4 citations


Journal ArticleDOI
William D. Mark1
TL;DR: In this article, the integral scale and intensity of a generic turbulence record is treated as a statistical problem of parameter estimation, and the method of maximum likelihood is used to estimate the scale of the von Karman transverse spectrum.
Abstract: Estimation of the integral scale and intensity of a generic turbulence record is treated as a statistical problem of parameter estimation. Properties of parameter estimators and the method of maximum likelihood are reviewed. Likelihood equations are derived for estimation of the integral scale and intensity applicable to a general class of turbulence spectra that includes the von Karman and Dryden transverse and longitudinal spectra as special cases. The method is extended to include the Bullen transverse and longitudinal spectra. Coefficients of variation are given for maximum likelihood estimates of the integral scale and intensity of the von Karman spectra. Application of the method is illustrated by estimating the integral scale and intensity of an atmospheric turbulence vertical velocity record assumed to be governed by the von Karman transverse spectrum.

4 citations


Journal ArticleDOI
TL;DR: In this article, the first two prior moments of the trend parameter were derived by using the solution of a WIENER-HOFF-type integral equation, based on continuous observations of a random field.
Abstract: Based on continuous observations of a random field and on the first two prior moments of the trendparameter is derived. essentially by use of the solution of a WIENER-HOFF-type integral equation.

2 citations


Journal ArticleDOI
Way Kuo1
TL;DR: In this article, a closed form Bayesian availability estimator is investigated through computer simulation, and the degree of bias and small variation of the estimator are obtained through computer simulations.

Journal ArticleDOI
TL;DR: In this paper, the authors present a physical interpretation of estimating the parameters of a linear functional relationship model from the stable equilibrium position of a mechanical system, and find that the estimates obtained from the physical model coincide with the maximum likelihood estimates.
Abstract: This paper presents a physical interpretation of estimating the parameters of a linear functional relationship model. The estimates are determined from the stable equilibrium position of a mechanical system. It is found that the estimates obtained from the physical model coincide with the maximum likelihood estimates.

Book ChapterDOI
01 Jan 1984
TL;DR: Bock as discussed by the authors presented an approach to adult height prediction based on fitting the triple-logistic growth function (Bock & Thissen, 1980) to individual height data, which is of importance, both to understand the implications of Bock's approach and to the following comments, that the significance of the maximum a posteriori (MAP) estimation of function parameters is realised.
Abstract: Bock presents an approach to adult height prediction based on fitting the triple-logistic growth function (Bock & Thissen, 1980) to individual height data. It is of importance, both to understanding the implications of Bock’s approach and to the following comments, that the significance of the Maximum A Posteriori (MAP) estimation of function parameters is realised. The present use of growth functions or models is made possible only in the presence of suitable data. These data must have more individual data points than the number of parameters in the function to be fitted. For a Preece-Baines Model 1 fit for example (Preece & Baines, 1978) at least 6 data points must be present to fit the 5 parameter model. Similarly for the 9 parameter triple-logistic (Bock & Thissen, 1980) at least 10 data points must be present. The satisfaction of these criteria poses obvious problems to research workers wanting to predict adult stature, interpolate or extrapolate data or derive biological parameters, such as peak height velocity, from functions fitted to few data points.

ReportDOI
01 Dec 1984
TL;DR: Two deterministic algorithms for the maximum a posteriori estimation of a one dimensional, binary Markov random field from noisy observations are presented and an experimental comparison of the performance of optimal algorithms with a stochastic approximation scheme is presented.
Abstract: : This document presents two deterministic algorithms for the maximum a posteriori estimation of a one dimensional, binary Markov random field from noisy observations. Extensions to other related problems, such as one dimensional signal matching, and estimation of continuous valued Markov random fields are also discussed. Finally, the author presents an experimental comparison of the performance of optimal algorithms with a stochastic approximation scheme (simulated annealing). Additional keywords: Mathematical models, Dynamic programming, Gaussian noise, White noise, Army research. (Author)

Proceedings ArticleDOI
01 Mar 1984
TL;DR: A motion compensated coding procedure based on a time modified autoregressive image source model that has the advantage that it does not depend on exact knowledge of the displacement vector is presented.
Abstract: In this paper we present a motion compensated coding procedure based on a time modified autoregressive image source model. The procedure has the advantage that it does not depend on exact knowledge of the displacement vector. Instead, a two step procedure for determining the displacement is employed. In the first step the nearest integer displacement for any particular block is determined using a maximum a posteriori (MAP) estimate. The second step utilizes regression techniques that determine the best estimate for the autoregressive parameters of the model. This supplies knowledge equivalent to the non-integer portion of the displacement. The results of applying the algorithm to a forty one frame sequence of images is discussed.

15 Nov 1984
TL;DR: In this paper, a new look is taken at the problem of estimating the phase and other parameters of a periodic waveform in additive Gaussian noise, and the maximum a posteriori probability criterion with signal space interpretation is used to obtain the structures of optimum and some suboptimum phase estimators for known constant frequency and unknown constant phase with an a priori distribution.
Abstract: Motivated by advances in signal processing technology that support more complex algorithms, a new look is taken at the problem of estimating the phase and other parameters of a periodic waveform in additive Gaussian noise. The general problem was introduced and the maximum a posteriori probability criterion with signal space interpretation was used to obtain the structures of optimum and some suboptimum phase estimators for known constant frequency and unknown constant phase with an a priori distribution. Optimal algorithms are obtained for some cases where the frequency is a parameterized function of time with the unknown parameters and phase having a joint a priori distribution. In the last section, the intrinsic and extrinsic geometry of hypersurfaces is introduced to provide insight to the estimation problem for the small noise and large noise cases.