Showing papers on "Maximum a posteriori estimation published in 1985"

A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions

Abstract: The method of maximum likelihood leads to an ill-posed optimization problem in the case of a mixture of normal distributions. Estimation in the univariate case is reformulated using simple constraints into an optimization problem having a strongly consistent, global solution.

Visual signal detection. III. On Bayesian use of prior knowledge and cross correlation.

Abstract: Experimental results are presented demonstrating that humans can make effective use of prior knowledge for detecting and identifying visual signals in static noise. The signals were selected from an orthogonal Hadamard set. There was a marked drop in detection performance when observers did not know which signal was present. The drop was in excellent quantitative agreement with that predicted by the theory of signal detectability. The statistical efficiency of the human observers was 33% in both cases (detection with and without prior knowledge). When interpreted in terms of channel uncertainty, the detection results demonstrated an upper limit of 10 orthogonal, uncertain channels. The statistical efficiency for the Hadamard signal-identification task was 40%. All the results are consistent with the standard theory of signal detectability based on a Bayesian maximum a posteriori probability decision strategy using cross correlation (or matched filtering) of expected signal profiles with those present in the display.

Motion Compensated Image Coding with a Combined Maximum A Posteriori and Regression Algorithm

Abstract: In this paper we present a method for motion compensated image coding based upon a two-step displacement estimation procedure. The first step utilizes a maximum a posteriori (MAP) estimator to determine the best integer displacement, while the second step requires solving for the regression coefficients that supply the same information as the noninteger portion of the displacement. This approach is a different and simplified procedure in that the integer displacement is measured first, and then a linear combination of only four values from the previous image, shifted by the measured integer displacement, is used. This procedure differs both from the ones which measure the displacement vector D first and interpolate the previous image, and from the ones which use only linear prediction. This method is derived and results are presented for two separate 40-frame digital image sequences. A sum of absolute error distortion measure is used to determine the optimal structure of the residual quantizer.

Sequential Estimation of Machinability Parameters for Adaptive Optimization of Machinability Data Base Systems

Abstract: Mathematical model type machinability data base systems require suitable model building procedures to estimate the model parameters. The estimation procedure should be capable of using subjective prior information about the models and must also be capable of adapting the model parameters to the particular machining environment for which the data are needed. In this paper, the sequential Maximum A Posteriori (MAP) estimation procedure is proposed as the mathematical tool for performing these functions. Mathematical details of this estimation procedure are presented. The advantages of this method over conventional regression analysis are discussed based on the analysis of an experimental tool life data set. Details regarding the selection of the various initial values needed for starting the sequential procedure are presented. The use of prior information about the models in order to improve the parameter estimates is investigated. The adaptive capability of the procedure is analyzed using simulated tool life data. The results of this analysis indicate that the proposed sequential estimation procedure is a valuable tool for estimating machinability parameters and for the adaptive optimization of machinability data base systems.

Optimal Bayesian Estimators For Image Segmentation and Surface Reconstruction

Abstract: A very fruitful approach to the solution of image segmentation and surface reconstruction tasks is their formulation as estimation problems via the use of Markov random field models and Bayes theory. However, the Maximuma Posteriori (MAP) estimate, which is the one most frequently used, is suboptimal in these cases. We show that for segmentation problems the optimal Bayesian estimator is the maximizer of the posterior marginals, while for reconstruction tasks, the threshold posterior mean has the best possible performance. We present efficient distributed algorithms for approximating these estimates in the general case. Based on these results, we develop a maximum likelihood that leads to a parameter-free distributed algorithm for restoring piecewise constant images. To illustrate these ideas, the reconstruction of binary patterns is discussed in detail.

Bayesian Point Estimation Using the Predictive Distribution

Abstract: There is considerable question about how a Bayesian might provide a point estimate for a parameter when no loss function is specified. The mean, median, and mode of the posterior distribution have all been suggested. This article considers a natural Bayesian estimator based on the predictive distribution of future observations. It is shown that for the set of parameters that admit an unbiased estimate, this predictive estimate coincides with the posterior mean of the parameter. It is argued that this result provides some justification for use of the posterior mean as a Bayesian point estimate when there is no loss structure.

Parameter Estimation for a Specific Software Reliability Model

Abstract: The problem of maximum likelihood estimation in the Jelinski-Moranda software reliability model is studied. The distribution of the stochastic variable that completely determines the maximum likelihood estimate is obtained. s-Confidence intervals for the parameter of interest can then be constructed by using the same stochastic variable. An example is given using real data.

Bayes Estimation of the Reliability Function of Normal Distribution

Abstract: Bayes estimates of the survivor function of the s-normal distribution are obtained using the predictive distribution and some recent results on Bayes approximations due to Lindley. Monte Carlo simulation was used. These estimates have smaller rms error than that of their maximum likelihood counterparts. Except for large samples, the exact estimators based on the predictive distribution perform better than the Lindley approximate estimators.

Empirical Bayes estimation in sampling inspection

Abstract: SUMMARY This paper considers an empirical Bayes approach to estimating the number of defectives in a hypergeometric distribution. It involves application of an empirical Bayes identity which has proved useful in providing simple Bayes estimates for various other models. Data on the reliability of coding the answers to questions from a household survey illustrate how an empirical Bayes estimate can be computed without knowledge of the prior distribution of the number of defectives.

Detection And Identification Efficiency: An Update

Abstract: In most previous studies of observer performance it has been assumed that the observer had complete a priori information about signal parameters and tasks have been performed using spatially constant backgrounds. Results will be presented for more complex tasks including identification of signals from an orthogonal set, signal edge location accuracy, detectability of negative contrast discs and detection of discs on sinusoidal and square wave luminance backgrounds. The effect of digital amplitude quantization will be shown to be predictable by a simple theory. It will also be shown that the standard assumption of a constant observer internal noise is incorrect. It has been found that internal noise is proportional to display noise when the display noise is easily visible. It is proposed that human performance is best described by a sub-optimal Bayesian decision strategy based on maximum a posteriori probabilities.

Approximate bayes estimation of reliability of two parameter inverse gaussian distribution

Abstract: This paper extends the result of Padgett (1981) and gives a Bayes estimate of the reliability function of two-parameter inverse Gaussian distribution using Jeffreys' non-informative joint prior and a squared error loss fun ction . A numerical example is given. Based on a Monte Carlo simulation, Bayes estimator of reliability is compared with its maximum likelihood counterpart.

Pseudo maximum likelihood estimation for the dirichlet-multinomial distribution

Abstract: Pseudo maximum likelihood estimation (PML) for the Dirich-let-multinomial distribution is proposed and examined in this pa-per. The procedure is compared to that based on moments (MM) for its asymptotic relative efficiency (ARE) relative to the maximum likelihood estimate (ML). It is found that PML, requiring much less computational effort than ML and possessing considerably higher ARE than MM, constitutes a good compromise between ML and MM. PML is also found to have very high ARE when an estimate for the scale parameter in the Dirichlet-multinomial distribution is all that is needed.

A note on the estimation of variances in state-space models using the maximum a posteriori procedure

Abstract: This note examines an estimation procedure for the unknown parameters in a state-space model proposed by Tsang, Glover, and Bach. The method is based on the maximum a posteriori (MAP) principle. Contrary to the claims of Tsang et al. it is shown that the algorithm performs very poorly compared to maximum likelihood. Some insight into the shortcomings of the MAP procedure is obtained by comparing it to the computation of maximum likelihood estimators by the EM algorithm.

Joint Pulse Spreading Estimation and Decoding in Stretched Pulse PPM Optical Channels

Abstract: In this paper, maximum a posteriori probability (MAP) decoding for a stretched-pulse, PPM, direct-detection optical communication system is examined when the spreading factor of the received laser pulse is unknown. Based on the discrete count model; joint pulse spreading estimators and decoders are derived for both Poisson and avalanche photodetection (APD) cases. Performance is evaluated in terms of probability of error for pulse decoding.

Maximum a posteriori array signal processing

Abstract: A noncausal estimator is presented for the position versus time sequence of a source relative to an array of passive receivers. The position is estimated in terms of the bearing and range of the source which are modelled as second order Gauss-Markov discrete time sequences. A maximum a posteriori estimation procedure is developed which provides for an exact nonlinear doppler compensated estimator of the position vector for a batch of received sensor data. The result is a delayed, smoothed position vector for the batch as opposed to a casual estimation filter output sequence. The signal spectrum is also estimated for detection purposes.

A MAP estimate that maximizes entropy—An alternative interpretation for an autoregressive model

Abstract: It is shown here that when extrapolation of a sequence of data with unknown statistics is performed under two optimization constraints, viz. maximizing the entropy and maximizing the a posteriori (MAP) probability density function (PDF) of the unknown sample, the resulting estimate is the same as that of an Autoregressive (AR) model. This leads to the conclusion that the estimate from an AR model is optimum in the sense that it is the MAP estimate which maximizes entropy.

An emplrical bayes approach in estimating the parameters of the or more geometric distributions

Abstract: The estimation of the parameters of two or more geometric distribuionsis considered by usinq an empirical Bayesian approach. Robbins (1983) gave empirical Bayes estimates if the number of distributions N is large, buthere we consider the cascwhore N is small. The parameters of the prior distribution areest imated by looking at maximum like lihood and momentest imation methods.