Showing papers on "Maximum a posteriori estimation published in 1978"

Nonparametric Maximum Likelihood Estimation of a Mixing Distribution

Abstract: The nonparametric maximum likelihood estimate of a mixing distribution is shown to be self-consistent, a property which characterizes the nonparametric maximum likelihood estimate of a distribution function in incomplete data problems. Under various conditions the estimate is a step function, with a finite number of steps. Its computation is illustrated with a small example.

Bayesian estimates of equation system parameters, An application of integration by Monte Carlo

Abstract: textMonte Carlo (MC) is used to draw parameter values from a distribution defined on the structural parameter space of an equation system. Making use of the prior density, the likelihood, and Bayes' Theorem it is possible to estimate posterior moments of both structural and reduced form parameters. The MC method allows a rather liberal choice of prior distributions. The number of elementary operations to be preformed need not be an explosive function of the number of parameters involved. The method overcomes some existing difficulties of applying Bayesian methods to medium size models. The method is applied to a small scale macro model. The prior information used stems from considerations regarding short and long run behavior of the model and form extraneous observations on empirical long term ratios of economic variables. Likelihood contours for several parameter combinations are plotted, and some marginal posterior densities are assessed by MC.

A new look at the Bayes procedure

Abstract: In developing an estimate of the distribution of a future observation it becomes natural and necessary to consider a distribution over the space of parameters. This justifies the use of Bayes procedures in statistical inference. An objective procedure of evaluation of the prior distribution in a Bayesian model is developed and the classical ignorance prior distribution is newly interpreted as the locally impartial prior distribution.

Bayesian Estimation of Parameters of Life Distributions and Reliability from Type II Censored Samples

Abstract: The Bayesian approach to reliability estimation from Type II censored samples is discussed here with emphasis on obtaining natural conjugate prior distributions. The underlying sampling distribution from which the censored samples are drawn follows a generalized life model (GLM) which includes a model proposed by Epstein and Sobel, Weibull, exponential, and Rayleigh distributions as special cases. Results are given for the Type II asymptotic distribution of largest values, Pareto, and Limited distribution. The natural conjugate prior, Bayes estimate for the generalized scale parameter, posterior risk, Bayes risk and Bayes estimate of the reliability function were derived for the distributions studied. In every case the natural conjugate prior is a 2-parameter family which provides a wide range of possible prior knowledge. Conjugate diffuse priors were derived. A diffuse prior, also called a quasi-pdf, is not a pdf because its integral is not unity. It represents roughly an informationless prior state of knowledge. The proper choice of the parameter for the diffuse prior leads to maximum likelihood, classical uniform minimum-variance unbiased estimator, and an admissible biased estimator with minimum mean square error as the generalized Bayes estimate. A feature of the GLM is the increasing function g(·) with possible applications in accelerated testing. KG(·) is a s-complete s-sufficient statistic for ?, and KG(·)/m is a maximum likelihood estimate for ?. Similar results were obtained for the Pareto, Type II asymptotic distribution of extremes, Pareto (associated with Pearl-Reed growth distribution) and others.

Notes on linear image restoration by maximizing the a posteriori probability

Abstract: A distinction is made between the minimum mean-square error estimate derived for the linear case of maximum a posteriori restoration and the common Wiener estimate. The linear MAP filter is shown to produce good results with less a priori knowledge than is required for the Wiener filter.

Image mensuration by maximum a posteriori probability estimation

Abstract: We present an algorithm for pulse width estimation from blurred and nonlinear observations in the presence of signal dependent noise. The main application is the accurate measurement of image sizes on film. The problem is approached by modeling the signal as a discrete position finite state Markov process, and then determining the transition location that maximizes the a posteriori probability. It turns out that the blurred signal can be represented by a trellis, and the maximum a posteriori probability (MAP) estimation is obtained by finding the minimum cost path through the trellis. The latter is done by the Viterbi algorithm. Several examples are presented. These include the measurement of the width of a road in an aerial photo taken at an altitude of 5000 ft. The resulting width estimate is accurate to within a few inches.

Estimation of LPC coefficients from speech waveforms degraded by additive random noise

Abstract: Application of a Maximum A Posteriori (MAP) estimation procedure in estimating the LPC coefficients from speech waveforms degraded by additive random noise generally leads to solving a set of non-linear equations which are computationally undesirable. However, an attempt to approximate the true MAP estimation procedure leads to two iterative methods that require solving only sets of linear equations. These two methods have been applied to real speech data degraded by additive white Gaussian noise, and in this paper some preliminary results are discussed.

Computational savings and implementation of maximum likelihood detectors (Corresp.)

Abstract: A further analysis of maximum likelihood sequence estimation algorithms for Gaussian channels with finite intersymbol interference is presented. It is shown that several maximum likelihood survivor paths cannot occur simultaneously, and hence that searching some of the nodes of the state trellis diagram can be avoided. An efficient algorithm is given that updates the metrics while avoiding redundant parts of the search.

Estimation of the Operating Characteristics of Item Response Categories II: Further Development of the Two-Parameter Beta Method.

Abstract: : The Two-Parameter Beta Method, introduced in the previous study as a method of estimating the operating characteristics of a test item, has proved to be as efficient as the Normal Approximation Method, for a set of simulated data of 500 hypothetical examinees having a uniform latent trait distribution between -2.475 and 2.475. Both methods are characterized: (1) by the use of a relatively small number of subjects-like 500 -- in the whole procedure of estimation; (2) without assuming any prior mathematical model; and (3) by the use of the estimated joint distribution of the latent trait and its maximum likelihood estimate. In the Two-Parameter Beta Method, the method of moments is adopted to approximate the probability density function of the maximum likelihood estimate, using polynomials of degree 3 and 4. The first two conditional moments of the latent trait, given the maximum likelihood estimate, are derived from theory and computed for the data for each value of the maximum likelihood estimate. The conditional distribution of the latent trait, given the maximum likelihood estimate, is approximated by a Beta distribution using the method of moments, with two a priori set parameters and two estimated parameters from the conditional moments.

Non-linear state estimation in observation noise of unknown covariance†

Abstract: The problem of estimating the state of a stationary Gauss-Markov sequence observed in uncorrelated Gaussian noise of constant, hut unknown, covarianee R is considered. A non-informative prior density is assigned to the prior innovations covarianco M, which is unknown by virtue of the uncertainty in R. The a posteriori density of M evolves as an inverted Wishart, censored to account for the fact that M is bounded from below by a positive definite matrix. The resulting non-linear state estimator involves a canonical integral which can be approximated to yield an attractive parallel filtering structure. The structure can be used to approximate the maximum a posteriori (MAP) estimate of the innovations covarianee,

On estimating the phase of a periodic waveform in additive Gaussian noise, part 1

Abstract: Motivated by recent advances in technology, a new look is taken at the problem of estimating the phase of a periodic waveform in additive Gaussian noise. The maximum a posteriori probability criterion with signal space interpretation is used to obtain the structures of optimum and some suboptimum phase estimators for the following cases: (1) known constant frequency and unknown constant phase with an a priori distribution; (2) unknown constant frequency and phase with a joint a priori distribution; (3) frequency a parameterized function of time with a joint a priori distribution on parameters and phase and (4) frequency a Gaussian random process.

Array Processor Performance Under Directional Uncertainty

Abstract: Detection performance of four candidate receiver structures for the signal known except for direction (SKED) array problem is investigated. Included are the Bayes optimal detector, two estimate and plug structures, and a fixed estimate structure. Estimators considered are the maximum likelihood (ML) and maximum a posteriori (MAP). Performance degradation from optimal for the estimate and plug structures considered is shown to be significantly more severe the larger the array size.

A time/speaker normalization technique for word verification

Abstract: The present approach for solving the word verification problem involves matching an input template with a known word reference template, The multidimensional template consists of formant values over the duration of the utterance. Due to speaking rate and idiosyncratic variations of speakers, both temporal and spectral normalizations are required. The time normalization technique employs a piecewise linear time warping function to map the unnormalized utterance into the normalized reference space. Pivot points used to align the input data template with the reference template are located in the utterance using maximum a posteriori (MAP) estimation. Statistics required to define the multidimensional density function for the estimator are obtained by training on known pivot point locations. Frequency normalization is then performed where the input template is linearly scaled (with a gain and bias) to minimize the weighted mean‐square error between the scaled input template and the reference template. This error in addition to the corresponding gain and bias terms are used in a metric for word verification.

Phase and symbol sequence decoding on random walk phase channels

Abstract: : Consider the problem of estimating phase and decoding data symbols from baseband data. Assume the phase sequence is a random walk on the circle and the symbols are drawn independently from an equiprobable alphabet for transmission over a perfectly equalized channel. A dynamic programming algorithm (Viterbi algorithm) is derived for decoding a maximum a posteriori (MAP) phase-symbol sequence on a finite dimensional phase-symbol trellis. Simulation results for binary and 8-ary phase modulated (PM) symbol sets are presented. (Author)