Showing papers on "Maximum a posteriori estimation published in 1983"

Survey of classical and bayesian approaches to the change-point problem: fixed sample and sequential procedures of testing and estimation

Abstract: Publisher Summary This chapter discusses fixed sample and the sequential procedures of testing and estimation and describes classical and Bayesian approaches to the change-point problem. It presents Bayesian and maximum likelihood estimation of the location of the shift points. The Bayesian approach is based on modeling the prior distribution of the unknown parameters, adopting a loss function and deriving the estimator, which minimizes the posterior risk. The chapter discusses this approach with an example of a shift in the mean of a normal sequence. The estimators obtained are generally nonlinear complicated functions of the random variables. From the Bayesian point of view, these estimators are optimal. The maximum likelihood estimation of the location parameter of the change point is an attractive alternative to the Bayes estimators. Regression relationship can change at unknown epochs, resulting in different regression regimes that should be detected and identified.

Bayesian approach to limited-angle reconstruction in computed tomography

Abstract: An arbitrary source function cannot be determined fully from projection data that are limited in number and range of viewing angle. There exists a null subspace in the Hilbert space of possible source functions about which the available projection measurements provide no information. The null-space components of deterministic solutions are usually zero, giving rise to unavoidable artifacts. It is demonstrated that these artifacts may be reduced by a Bayesian maximum a posteriori (MAP) reconstruction method that permits the use of significant a priori information. Since normal distributions are assumed for the a priori and measurement-error probability densities, the MAP reconstruction method presented here is equivalent to the minimum-variance linear estimator with nonstationary mean and covariance ensemble characterizations. A more comprehensive Bayesian approach is suggested in which the ensemble mean and covariance specifications are adjusted on the basis of the measurements.

An estimation-theoretic approach to terrain image segmentation

Abstract: A method for modeling images of natural terrain is developed and applied to the segmentation of aerial photographic data. An underlying stochastic structure based on linear filtering concepts provides a means of modeling the terrain in local areas of the image. Superimposed on this is a Markov random field that describes transitions from regions of one terrain type to another. Maximum likelihood and maximum a posteriori estimation are applied to estimate regions of similar terrain. Results of application to digitized aerial photographs are presented and discussed.

Maximum likelihood estimation of order m for stationary stochastic processes

Abstract: Sometimes the likelihood cannot be computed even introducing approximations whose effect is asymptotically negligible. To overcome this problem for inference from a stochastic process, we approximate the log likelihood by a sum whose generic term is the density function of the corresponding sample element conditional on the m most recent observations, for some m >s 0. General results on the asymptotic properties of the associated estimates are given, and numerical comparisons with other estimators are carried out in special cases.

Estimation of recombination frequency in genetic linkage studies.

Abstract: A binomial-like model is developed that may be used in genetic linkage studies when data are generated by a testcross with parental phase unknown. Four methods of estimation for the recombination frequency are compared for data from a single group and also from several groups; these methods are maximum likelihood, two Bayesian procedures, and an ad hoc technique. The Bayes estimator using a noninformative prior usually has a lower mean squared error than the other estimators and because of this it is the recommended estimator. This estimator appears particularly useful for estimation of recombination frequencies indicative of weak linkage from samples of moderate size. Interval estimates corresponding to this estimator can be obtained numerically by discretizing the posterior distribution, thereby providing researchers with a range of plausible recombination values. Data from a linkage study on pitch pine are used as an example.

Restoration of bilinearly distorted images: II. Bayesian method

Abstract: Bayesian estimation methods are applied to the problem of restoring a distorted noisy image. The distortion system is assumed bilinear, i.e., quadratic and with nonzero spread. Noise is Gaussian, additive, and signal independent. An algorithm for determining the maximum a posteriori probability restored image is determined by using the steepest-ascent method. Results are applied to one- and two-dimensional images in a partially coherent diffraction-limited system, and the effect of coherence and noise on image restorability is assessed.

Estimation of parameters in the marginal fisher distribution1

Abstract: Summary The Fisher distribution is frequently used as a model for the probability distribution of directional data, which may be specified either in terms of unit vectors or angular co-ordinates (co-latitude and azimuth). If, in practical situations, only the co-latitudes can be observed, the available data must be regarded as a sample from the corresponding marginal distribution. This paper discusses the estimation by Maximum Likelihood (ML) and the Method of Moments of the two parameters of this marginal Fisher distribution. The moment estimators are generally simpler to compute than the ML estimators, and have high asymptotic efficiency.

Dynamic speaker adaptation for isolated letter recognition using MAP estimation

Abstract: A dynamic speaker-adaptation algorithm for the C-MU feature-based isolated letter recognition system, FEATURE, is described. The algorithm, based on maximum a posteriori probability estimation techniques, uses the labelled observations input thus far to the classifier, as well as the a priori correlations of the features within and across the various letters or sets of letters (classes). The probability density functions (pdf) of all the classes are updated simultaneously rather than on a class-by-class basis so that the pdf of a given class is updated before any observation from that class has been input. A significant improvement in the recognition performance was observed for different vocabularies as the system tuned to the the characteristics of a new speaker. Finally, the algorithm was compared to simpler forms of dynamic adaptation. It produced a faster decrease of the error rate than the other tuning procedures. After a small number of iterations, however, the various procedures yielded similar results.

Constrained Maximum Likelihood Estimation of Initial Population Statistics from an Ensemble of Kalman Smoother Estimates

Abstract: A method is presented for constrained maximum likelihood estimation of the initial mean and covariance of an otherwise known linear discrete time dynamical system. An obvious technique to use is to obtain Kalman smoother estimates of the initial conditions for each of a series of tests and then combine them into an estimate of the initial distribution. This may be implemented either as a special case of the Expectation-Maximization (EM) or Scoring methods of statistical parameter identification. It is shown here that constraints can be added which improve convergence and identifiability in practical applications. This is accomplished via a hybrid EM/Scoring algorithm which combines the best features of both approaches.

Maximum likelihood estimation of the logarithmic series distribution

Abstract: This paper discusses the maximum likelihood estimation of the parameter of the logarithmic series distribution. The univariate case is treated in Part I, the multivariate case in Part II. A simple numerical estimation procedure is suggested using a fixed point approach. Convergence to the maximum likelihood estimator is shown. In Part III convergence rate is proven to be linear which is also demonstrated through example. In addition, comparisons with Newton’s method and the secant method in the univariate case, and with Newton’s method and the projected gradient method in the multivariate case are provided.

Comments on "A Map Symbol Synchronizer Implemented with Charge-Coupled Devices"

Abstract: We show that the synchronizer described in the above paper is not a maximum a posteriori (MAP) synchronizer, as it searches the minimum instead of the maximum of the log likelihood ratio. Only a slight modification is required to transform it into a MAP synchronizer. By a theoretical analysis, we show that this modification substantially reduces the rms timing error.

On two-stage parameter estimation in static system

Abstract: The general two-stage estimation idea is described. Maximum likelihood and maximum a posteriori probability methods for two-stage estimation are presented. The estimation algorithms for simple cases are given. The comparison of the direct and two-stage estimation is discussed.

On the Sampling Distribution of the Mode and Its Use with Standard Times

Abstract: The mode - the most likely value—of the distribution of task times is proposed as the definition of the standard time in certain nonmanufacturing applications. Three objectives of the use of time standards are discussed: personnel motivation and control, short-term work scheduling, and medium-range manpower planning. While the mean is the appropriate measure for the second and third, the mode may be preferable for the first. The sampling distributions of two estimators of the mode of the gamma distribution are investigated. A definition based on the maximum likelihood estimators of the distributional parameters is relatively easy to implement and has a much smaller sampling variance than the Pearson mode.

Improved maximum likelihood method for two-dimensional spectral estimation

Abstract: In this paper, we present a new method for two-dimensional spectral estimation This method is based on the extension of the relationship that exists between the maximum likelihood method and the maximum entropy method for one-dimensional signals to two-dimensional signals This method has a computational requirement similar to that of the maximum likelihood method, but has a resolution property which is considerably better than that of the maximum likelihood method Examples are shown to illustrate the performance of the new algorithm

A Computationally Efficient Fourier Domain Maximum A Posteriori Algorithm For Restoration Of Non-linearly Degraded Images

Abstract: A computationally efficient Fourier domain maximum a posteriori (MAP) algorithm is derived and implemented for restoration of a class of non-linearly degraded images. The proposed Fourier domain MAP restoration algorithm is shown to be approximately twice as efficient computationally as the extant spatial domain MAP restoration algorithm.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A comparison of distance measures for text-independent speaker identification

Abstract: A survey of research efforts in the area of speaker recognition indicate that for the same choice of speaker-dependent speech parameters the recognition accuracy is significantly affected by the distance measure used. In this work several distance classifiers are evaluated for use in text-independent speaker identification. The four distance measures investigated are the Mahalanobis distance, maximum a posteriori probability, nearest neighbor criterion and the correlation distance measure. It is found that both the maximum a posteriori probability criterion and the correlation distance measure yield extremely poor results. The Mahalanobis distance and the nearest neighborhood criterion yield relatively poor results (error \sim20-30 %) with the former consistently superior to the latter. It is shown that these scores can be improved through a proposed variation of the nearest neighbor method.

Bayesian estimation for compound weibull model

Abstract: This paper is concerned with the Bayesian estimation problem of the unknown parameters of the compound Weibull model with unequal shape parameter. Bayesian estimates are obtained for the uniform and gamma prior probability densities assumming independent prior distributions. Bayesian results in the case of compound Weibull model with equal shape parameter and in the case of one cause of failure models can be obtained as special cases from our result.Numerical comparison between the maximum likelihood and Bayes' estimates has been carried out using random numbers and computer facilities. Most of the Bayes' estimates are more efficient than the maximum likelihood estimates.