Showing papers on "Maximum a posteriori estimation published in 1979"

Maximum Likelihood Estimation of Observer Error-Rates Using the EM Algorithm

Abstract: In compiling a patient record many facets are subject to errors of measurement. A model is presented which allows individual error-rates to be estimated for polytomous facets even when the patient's "true" response is not available. The EM algorithm is shown to provide a slow but sure way of obtaining maximum likelihood estimates of the parameters of interest. Some preliminary experience is reported and the limitations of the method are described.

Maximum likelihood estimation of Hawkes′ self-exciting point processes

Abstract: A maximum likelihood estimation procedure of Hawkes' self-exciting point process model is proposed with explicit presentations of the log-likelihood of the model and its gradient and Hessian. A simulation method of the process is also presented. Some numerical results are given.

A dynamic programming algorithm for phase estimation and data decoding on random phase channels

Abstract: : The problem of simultaneously estimating phase and decoding data symbols from baseband data is posed. The phase sequence is assumed to be a random sequence on the circle and the symbols are assumed to be equally-likely symbols transmitted 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. A new and interesting principle of optimality for simultaneously estimating phase and decoding phase-amplitude coded symbols leads to an efficient two step decoding procedure for decoding phase-symbol sequences. Simulation results for binary, 8- ARY PM, and 16-QASK symbol sets transmitted over random walk and sinusoidal jitter channels are presented, and compared with results one may obtain with a decision-directed algorithm, or with the binary Viterbi algorithm introduced by Ungerboeck. When phase fluctuations are severe, and the symbol set is rich (as in 16-QASK), MAP phase-symbol sequence decoding on circles is superior to Underboeck's technique, which in turn is superior to decision-directed techniques.

Improved Methods of Maximum a Posteriori Restoration

Abstract: An improved numerical solution method for maximum a posteriori image restoration is presented. Results of the use of this method are shown to be superior to previous MAP restorations and equal or better than some common linear restorations. A natural convergence criterion is defined and shown to be a good indicator of restoration quality. The effects of the parameters of the MAP restorations are discussed.

Estimating the Parameters of the Beta-Binomial Distribution:

Abstract: For some situations the beta-binomial distribution might be used to describe the marginal distribution of test scores for a particular population of examinees. To use this distribution it is necessary to estimate two parameters which characterize the beta-binomial model. One method of estimating these parameters is to approximate the maximum likelihood estimates using some appropriately chosen iterative technique. When the number of examinees is small, however, it is not clear that this method of estimation is justified since the iterative approximations might not converge to the maximum likelihood estimate. Using Monte Carlo techniques, this paper compares the Newton-Raphson approximation to the maximum likelihood estimate with several other possible procedures. It is found that the Newton-Raphson method should be used when it yields admissible (positive) results.

Position Finding with Prior Knowledge of Covariance Parameters

Abstract: Butterly [1] presents a Bayesian approach as an alternative to the classical methods for solving the position-finding problem. Butterly assumes that bearing errors are independent and normally distributed with known variances. In the paper, the assumption of known variances is relaxed and it is shown that uncertainty about these variances can be incorporated into the model while also retaining the computational advantages of the Butterly formulation. It is also shown that the Bayes estimate and the classical maximum likelihood estimate will agree in certain cases.

Probability Density of the Maximum Likelihood Elevation Estimate of Radar Targets

Abstract: The probability density of the maximum likelihood estimate of elevation angle of a radar target in the presence of multipath is calculated. For detectable signals that have low signal-to-noise ratios, the density is a mixture of a Gaussian density and a delta function at the horizon.

A modification of the secant rule derived from a maximum likelihood principle

Abstract: An estimate of a zero of a complex function, constructed from ordinate information at distinct abscissae, is found from a Maximum Likelihood estimate relative to a normal probability distribution induced by a weak Gaussian distribution on a related Hilbert space. In the case of two ordinate observations this leads to an estimator structurally similar to the Secant Rule, and asymptotically approaching that rule in certain limiting situations. A correspondingly modified version of Newton's method is also derived, and regional and asymptotic convergence results proved.

Application of Bayesian Techniques to Reliability Demonstration, Estimation and Updating of the Prior Distribution.

Abstract: : A method is presented for the estimation of the shape and scale parameters of an inverted gamma prior distribution of the mean-time-to-failure for equipment having exponential time-to-failure distribution. This method, akin to the Maximum Likelihood Method, allows the use of all sorts of existing failure data on the equipment in question, provided a certain sufficient condition is satisfied. Further, this method (we call it the Generalized Maximum Likelihood Method) is usable to update the prior distribution, when new failure data become available. In the long run, this updating process will give rise to a solid prior, which can confidently be used in Reliability Demonstration. Various facets of the sufficient condition for the applicability of this estimation method are exposed, the variance--covariance matrix of the estimators is given under various randomness assumptions and some numerical considerations are discussed. There is a brief discussion of alternate estimators in the case of a truncated test data. (Author)