Showing papers on "Maximum a posteriori estimation published in 1974"

Multilevel discrete time system identification in large scale systems

Abstract: Hierarchical decomposition is considered to be one of the most powerful and offective tools to deal with complexity. Hierarchical system theory, which deals with system decomposition and coordination, can be used to decentralize and reduce the computational efforts requirements for many large-scale problems. This is achieved by decomposing the original system problem into several lower order easier to handle sub-problems, which are then coordinated such that the overall system objectives are met. In this work a hierarchical system theory approach to the discrete-time system identification problem is considered for stochastic large-scale system applications. A set of sequential discrete-time hierarchical identification algorithms, suitable for known and unknown system noise moments, are first obtained using a maximum a posteriori (MAP) approach with covariance matching and maximum likelihood (ML) methods. This is conducted in a two level hierarchical structure with two principles of coordination. ...

Maximum likelihood estimation in the birth-and-death process

Abstract: : Maximum likelihood estimation of the parameters lambda and mu of a simple (linear) birth-and-death process observed continuously over a fixed time interval is studied. Asymptotic distributions for large initial populations and for large periods of observation are derived and some nonstandard results appear. The related problem of estimation from the discrete skeleton of the process is also discussed.

On estimation and testing for the folded normal distribution

Abstract: For the folded normal distribution, generated froma N(μσ2) by loss of the signs of observations, μ=o corresponds to a non-regular case of estimation and testing. The large sample behaviour of the maximum likelihood estimate in this non-regular case is investigated. If σ is known, the estimate of μ is consistent at a rate of convergence of order n-1/4; if 0 is unknown the rate is or order n-1/8, as the sample size n tends to infinity. As a by-product it is shown that a moment method of estimation proposed by Elandt (1961) is locally asymptotically(as μ/σ→ 0 and n→∞).equivalent to the maximum likelihood method. Tests ofμ=0 are derived from the point of view of local optimality. In direct correspondence to the slow consistency of the estimates, the tests have very slowly increasing power functions.

The estimation of ρ in the first‐order autoregressive model: A Bayesian Approach

Abstract: Three general approaches to derive marginal posterior probability density functions for the autocorrelation coefficient of the first-order normal autoregressive model are presented, from which Bayes estimators can be obtained for a given loss function. The different approaches are based on varying assumptions about the incidental parameters of the model and are shown numerically to be approximately equivalent with respect to their mean and variance. A comparison is made between the Bayes estimator and some classical estimators on the basis of the risk function and the expected risk. The risk functions are determined by Monte Carlo methods for quadratic, symmetric linear, and various asymmetric linear loss functions. The Bayes estimators are shown to be considerably advantageous, especially when the sample size is small. The Bayes estimators are also shown to be extremely robust under changes of the loss function.

On the Sampling Properties of Bayesian Point Estimators

Abstract: The sampling distributions of various Bayesian point estimators are examined and it is shown that by choosing an appropriate prior distribution for the unknown parameter such estimators can be less biased than the maximum likelihood estimator. It is also shown that a pivotal quantity can be developed by a suitable transformation of the unknown parameter.

Quantum Bayes estimation of the amplitude of a coherent signal (Corresp.)

Abstract: The complex amplitude of a coherent quantum signal in the presence of thermal noise is to be estimated when its real and imaginary parts have a Gaussian prior distribution. Cost functions of Gaussian, power-law, and delta-function forms are shown all to lead to the same optimum estimator.

Maximum Likelihood Methods

Abstract: In dealing with the problem of estimating the parameters of a structural system of equations, we had not, in previous chapters, explicitly stated the form of the density of the random terms appearing in the system. Indeed, the estimation aspects of classical least squares techniques and their generalization to systems of equations are distribution free, so that no explicit assumption need be made with respect to the distribution of the error terms. On the other hand, in considering various tests of significance on 2SLS or 3SLS estimated parameters of a structural system, we have occasionally found it convenient to assert (joint) normality of the structural error terms. Under this assumption, the derivation of the asymptotic distribution of such estimators is simplified considerably.

Measurement of the relative delay between signals propagating in a multipath environment

Abstract: The problem of measuring the relative delay from a composite signal in additive noise is considered. The performance of standard autocovariance, nonlinear spectral analysis (cepstrum), and the delay-locked loop is analyzed and compared to the results of maximum a posteriori estimation. Comparison is based on: ability to detect a multipath situation, accuracy of the delay measurement, and resolution. Under conditions typically encountered in practice, cepstrum is shown to provide near optimum estimates. The relative ability of cepstrum and standard autocovariance to extract delay measurements is demonstrated by the results of an underwater experiment performed under conditions where the acoustic signal propagates along a direct and reflected path.