Showing papers on "Maximum a posteriori estimation published in 1972"
TL;DR: In this paper an approximation that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations is discussed and applied to the solution of the nonlinear filtering problem.
Abstract: Knowledge of the probability density function of the state conditioned on all available measurement data provides the most complete possible description of the state, and from this density any of the common types of estimates (e.g., minimum variance or maximum a posteriori) can be determined. Except in the linear Gaussian case, it is extremely difficult to determine this density function. In this paper an approximation that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations is discussed and applied to the solution of the nonlinear filtering problem. In particular, it is noted that a weighted sum of Gaussian probability density functions can be used to approximate arbitrarily closely another density function. This representation provides the basis for procedure that is developed and discussed.
1,267 citations
TL;DR: Recently, Malik [6, 7] has done classical maximum likelihood estimation as well as Bayesian estimation of the index parameter v of a Pareto distribution with density function as mentioned in this paper, and
Abstract: Recently, Malik [6, 7] has done classical maximum likelihood estimation as well as Bayesian estimation of the index parameter v of a Pareto distribution with density function
62 citations
TL;DR: In this paper, the authors studied the asymptotic behavior of the joint distribution and moments of generalized Bayesian estimates, maximum likelihood estimates and maximum probability estimates with respect to intervals constructed from independent observations with a density having a discontinuity of the first kind.
Abstract: In this paper the authors study the asymptotic behavior of the joint distribution and moments of generalized Bayesian estimates, maximum likelihood estimates and maximum probability estimates with respect to intervals constructed from independent observations with a density having a discontinuity of the first kind. Bibliography: 9 entries.
14 citations
13 citations
TL;DR: In this paper, the authors proposed a modification of the usual least square criterion for estimation in order to suppress bad data and showed that similar estimators can be obtained from maximum likelihood theory.
Abstract: Merrill and Schweppe [1] propose a modification of the usual least squares criterion for estimation in order to suppress bad data. It is shown that similar estimators can be obtained from maximum likelihood theory.
12 citations
TL;DR: In this article, the aeromagnetic field is assumed to be a Gaussian random function and the probability density function of the log-radial spectrum is shown to be an asymmetric non-Gaussian function.
Abstract: Starting from the assumption that the aeromagnetic field is a Gaussian random function the probability density function of log-radial spectrum is shown to be a slightly asymmetric non-Gaussian function, [2q/2 Γ(q/2)]−1q(q/2)−1 exp(q/2(r-exp(r))). The depth to magnetic layer is determined by maximum likelihood (ML) technique and is compared with the least square (LS) estimate. The difference between the two is only marginal, about 15%. The least square estimate is lower than the maximum likelihood estimate.
11 citations
TL;DR: In this article, a Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators.
Abstract: For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.
9 citations
TL;DR: In this article, empirical Bayes estimation procedures are introduced and employed to obtain an estimator for the unknown random scale parameter of a two-parameter Weibull distribution with known shape parameter.
Abstract: In part I empirical Bayes estimation procedures are introduced and employed to obtain an estimator for the unknown random scale parameter of a two-parameter Weibull distribution with known shape parameter. In part II, procedures are developed for estimating both the random scale and shape parameters. These estimators use a sequence of maximum likelihood estimates from related reliability experiments to form an empirical estimate of the appropriate unknown prior probability density function. Monte Carlo simulation is used to compare the performance of these estimators with the appropriate maximum likelihood estimator. Algorithms are presented for sequentially obtaining the reduced sample sizes required by the estimators while still providing mean squared error accuracy compatible with the use of the maximum likelihood estimators. In some cases whenever the prior pdf is a member of the Pearson family of distributions, as much as a 60% reduction in total test units is obtained. A numerical example is presented to illustrate the procedures.
8 citations
5 citations
TL;DR: The work is an extension of known results to the case in which the statistical description of the observed process may be nonstationary and implies that the optimality properties usually attributed to Bayes estimates can be attributed in some cases to maximum-likelihood estimates as well.
Abstract: It is shown that for a class of cost functions and a class of a priori distributions on the parameters to be estimated, the risks associated with the Bayes and maximum-likelihood estimates of the signal parameters become equal as the number of observations becomes large. This implies that the optimality properties usually attributed to Bayes estimates can be attributed in some cases to maximum-likelihood estimates as well. The work is an extension of known results to the case in which the statistical description of the observed process may be nonstationary.
5 citations
TL;DR: This paper purports to review the relations between the previously mentioned quantities in time-discrete communications, to conjecture a functional dependence of bias and MSE on the value of the transmitted parameter, and to present some results of a Monte-Carlo simulation that tests these conjectures.
Abstract: In above-threshold communication situations, the estimation bias and hence the modulation suppression are practically negligible; so that the output signal-to-noise ratio (SNR) is numerically very close to the reciprocal of the normalized mean-square error (MSE). The two last performance measures are, however, conceptually distinct as well as numerically widely different below threshold. Whereas in estimation and control problems the latter is of primary interest, much effort having been invested in its calculation and bounding, the former is very often more meaningful when transmitting sampled continuous data. This paper purports to review the relations between the previously mentioned quantities in time-discrete communications; to conjecture a functional dependence of bias and MSE on the value of the transmitted parameter, that simplifies these relations; to present some results of a Monte-Carlo simulation that tests these conjectures and provides performance curves for the maximum a posteriori probability, the (minimum-MSE-optimal) conditional mean and other derived estimators; and finally to speculate about the relative merits of these averaging type estimators as compared with the discriminator types in a frequency-position-modulation system, from the point of view of the aural character of the output noise below threshold.
TL;DR: This paper analyzes a hybrid navigation concept that uses signals from a radio interferometer mounted on a spinning geostationary satellite, preliminary position estimates from self-contained equipment, and stored a priori information on the past performance of this equipment.
Abstract: This paper analyzes a hybrid navigation concept that uses signals from a radio interferometer mounted on a spinning geostationary satellite, preliminary position estimates from self-contained equipment, and stored a priori information on the past performance of this equipment. The craft-borne processor, optimum in the maximum a posteriori (MAP) sense, is designed to estimate position coordinates using only the incoming radio signals, although improved estimates result if the other two items are available. An error analysis starts with the derivation of an estimation error covariance matrix, whose elements depend on additive receiver noise and the physical parameters of the system. A minimum 1? estimation error in position is obtained by trading off these parameters. The effects of other major error sources, such as tropospheric phase fluctuations, multipath, and craft altitude uncertainty, are added to the estimation error to give a total 1? position error on the order of 3.7 to 5.6 km.
TL;DR: In this paper, a binary frequency-shift-keying (FSK) communication system with an adaptive receiver is considered and partially coherent detection is accomplished exploiting phase and bit synchronization directly extracted from the information-bearing waveform.
Abstract: This paper considers a binary frequency-shift-keying (FSK) communication system with an adaptive receiver. Partially coherent detection is accomplished exploiting phase and bit synchronization directly extracted from the information-bearing waveform. The optimum (maximum a posteriori probability criterion) estimators of the relevant channel parameters are found along with some suboptimum realizations. It turns out that these schemes are decision-directed tracking systems that may be implemented using standard circuitry.
01 Jun 1972
TL;DR: In this article, the effects of prior data on a Bayesian analysis are studied, and the results of the many simulated trails are then analyzed to show the region of criticality for prior information being supplied to the Bayesian estimator.
Abstract: The critical point of any Bayesian analysis concerns the choice and quantification of the prior information. The effects of prior data on a Bayesian analysis are studied. Comparisons of the maximum likelihood estimator, the Bayesian estimator, and the known failure rate are presented. The results of the many simulated trails are then analyzed to show the region of criticality for prior information being supplied to the Bayesian estimator. In particular, effects of prior mean and variance are determined as a function of the amount of test data available.