Showing papers on "Maximum a posteriori estimation published in 1971"
01 Nov 1971
TL;DR: In this paper, the authors study the asymptotic behavior of certain tests of significance which can be based on maximum-likelihood estimators and show that the true parameter point, in estimation problems, lies on the boundary of the parameter space.
Abstract: The origin of the present paper is the desire to study the asymptotic behaviour of certain tests of significance which can be based on maximum-likelihood estimators. The standard theory of such problems (e.g. Wald(4)) assumes, sometimes tacitly, that the parameter point corresponding to the null hypothesis lies inside an open set in the parameter space. Here we wish to study what happens when the true parameter point, in estimation problems, lies on the boundary of the parameter space.
149 citations
47 citations
IBM1
TL;DR: A maximum a posteriori probability (MAP) approach is used to derive the optimal equalizer for binary signals transmitted at a constant rate over a dispersive and noisy channel and two suboptimal nonlinear equalizers are obtained.
Abstract: A maximum a posteriori probability (MAP) approach is used to derive the optimal equalizer for binary signals transmitted at a constant rate over a dispersive and noisy channel. The optimal equalizer is shown to consist of a matched filter followed by a very complex nonlinear transversal filter. Various approximations are made to simplify the transversal filter. Thus the optimal linear equalizer and two suboptimal nonlinear equalizers are obtained. The performance characteristics of these equalizers are compared in terms of eye patterns and error probabilities. These investigations exhibit a clear superiority of the nonlinear equalizers. Up to a certain peak distortion, intersymbol interference can be eliminated by nonlinear equalization With negligible noise enhancement. The error probability then closely approaches the error probability in the case of noninterfering signals.
40 citations
TL;DR: In this paper, a minimum variance linear sequential estimation algorithm, developed by maximum a posteriori likelihood techniques, is given for the case where the current measurement noise, v(k), is correlated with the plant noise of the previous stage, w(k-1).
9 citations
01 Jan 1971
TL;DR: It is shown that a certain weighted average of the prior distribution and the empirical distribution yields an estimate of the posterior distribution that is consistent with Bayes' theorem.
Abstract: It is shown that a certain weighted average of the prior distribution and the empirical distribution yields an estimate of the posterior distribution that is consistent with Bayes' theorem. A comparison of this approach and conventional parametric Bayesian estimation is made for some specific cases.
5 citations
01 Jan 1971
TL;DR: In this paper, it is shown that the estimation formulae are often of high degree polynomials, is only correct for a few cases and in the event can be side-stepped by the use of scores.
Abstract: It is possible to develop a number of systems of estimation and nowhere does this seem to be more true than for the estimation of genetic crossover fractions. Several of these fail dismally because of inaccuracy and inefficiency (Fisher and Balmukand, 1928). Others have received consideration in the main because of their interesting and special features. These exceptional systems are known as minimum χ2, product ratio, and minimum discrepancy (Fisher and Balmukand, 1928; Immer, 1930; Haldance,1953; Murty, 1954b). The most versatile and efficient system, however, is the method of maximum likelihood (Fisher, 1922; Mather, 1951; Bailey, 1961). The main objection to the method, namely, that the estimating formulae are often of high degree polynomials, is only correct for a few cases and in the event can be side-stepped by the use of scores.
1 citations