Showing papers on "Maximum a posteriori estimation published in 1976"

Maximum likelihood estimation for continuous-time stochastic processes

Abstract: This paper is mainly concerned with the asymptotic theory of maximum likelihood estimation for continuous-time stochastic processes. The role of martingale limit theory in this theory is developed. Some analogues of classical statistical concepts and quantities are also suggested. Various examples that illustrate parts of the theory are worked through, producing new results in some cases. The role of diffusion approximations in estimation is also explored. MAXIMUM LIKELIHOOD ESTIMATION; CONTINUOUS-TIME STOCHASTIC PROCESSES; ASYMPTOTIC THEORY; MARTINGALE LIMIT THEORY; DIFFUSION APPROXIMATIONS

Maximum a Posteriori Estimation of Position in Scintillation Cameras

Abstract: We derive the form of the maximum likelihood (ML) estimate of the location of the scintillation point given the photomultiplier counts in an Anger Scintillation camera. This estimate is also Maximum a Posteriori (MAP) if the prior probability density on the scintillation point is uniform in the object plane. The form of the estimate suggests the possibility of an optical filtering implementation. We note that the ML estimate implies a solution that is remarkably similar to the "optimum position arithmetic" derived by Tanaka, et al.

Performance of Bayesian parameter estimators for linear signal models

Abstract: In this short paper the Bayesian estimation of parameters of discrete time, linear, finite-dimensional stochastic systems is discussed. Upper bounds for the estimator mean-square error are obtained under the assumption of a finite parameter set. Necessary and sufficient conditions are established for exponential convergence of the Bayesian estimate to the true parameter values in the mean-square error sense for systems with measurements which are stationary Gaussian random processes. The conditions for convergence are given in terms of a finite set of signal model Markov parameters. The performance results for parameter estimation are shown to yield bounds on the performance of the nonlinear state estimators for the class of signal models under discussion.

Maximum likelihood estimation for stochastic processes - a martingale approach

Abstract: This thesis is primarily concerned with the investigation of asymptotic properties of the maximum likelihood estimate (MLE) of parameters of a stochastic process. These asymptotic properties are related to martingale limit theory by recognizing the (known) fact that, under certain regularity conditions, the derivative of the logarithm of the likelihood function is a martingale. To this end, part of the thesis is devoted to using or developing martingale limit theory to provide conditions for the consistency and/or asymptotic normality of the MLE. Thus, Chapter 1 is concerned with the martingale limit theory, while the remaining chapters look at its application to three broad types of stochastic processes. Chapter 2 extends the classical development of asymptotic theory of MLE's (a la Cramer [/]) to stochastic processes which, basically, behave in a non-explosive way and for which non-random norming sequences can be used. In this chapter we also introduce a generalization of Fisher's measure of information to the stochastic process situation. Chapter 3 deals with the theory for general processes develops the notion of \"conditional\" exponential families of processes, as well as establishing the importance of using random norming sequences. In Chapter it we consider the asymptotic theory of maximum likelihood estimation for continuous time processes and establish results which are analogous to those for discrete time processes. In each of these chapters many applications are considered in an attempt to show how known and new results fit into the general

A probability diversity combiner for digital h.f. transmission

Abstract: The switched a posteriori probability (s.a.p.) diversity combiner has equivalent performance to maximum a posteriori probability (m.a.p.) combiner for dual diversity when binary transmission is used. Moreover, it is much simpler to implement since it is similar in principle to the conventional switched diversity combiner. The difference is that instead of switching to the branch with the highest signal-to-noise ratio, the switching is done between the branches on a bit-by-bit basis and to the branch which is most likely to be correct about what was sent. Some examples of impulse noise are used to show the difference between the m.a.p. (or s.a.p.) methods and the conventional methods of maximal ratio combining, selector branch combining, and no diversity, in terms of average error probability. The examples also illustrate the different processing that is done on the signals by the different methods. One possible method of implementing the s.a.p. technique is proposed for the case of 4-phase p.s.k. with differential encoding.

Empirical Bayes interval estimation

Abstract: Summary An empirical Bayes approach to interval estimation of an unknown parameter λ of a univariate data distribution is formulated, with special reference to some specific parametric forms of the data distributions and prior distributions. The connection with the notion of tolerance limits is traced.