Showing papers on "Expectation–maximization algorithm published in 1970"

The efficient use of function minimization in non-linear maximum-likelihood estimation

Abstract: Maximum‐likelihood estimation problems can be solved numerically using function minimization algorithms, but the amount of computing required and the accuracy of the results depend on the way the algorithms are used. Attention to the analytical properties of the model, to the relationship between the model and the data, and to descriptive properties of the data can greatly simplify the problem, sometimes providing a method of solution on a desk calculator. This paper describes how parameter transformation, sequential minimization and nested minimization can be used to solve particular problems. Applications to well‐known problems of distribution fitting, quantal responses and least‐squares curve fitting are described. The implications for computer programming are discussed.

Maximum likelihood estimation of a unimodal density. II

Abstract: This paper is a sequel to the earlier paper, "Maximum Likelihood Estimation of a Unimodal Density Function." The MLE of a unimodal density with unknown mode is shown to agree, for sufficiently large $n$ and on certain regions, with the MLE of a unimodal density with known mode. The asymptotic distributions of the MLE's then agree. Also a geometrical interpretation of the MLE of a unimodal density with unknown mode is given.

Inferences for the Cauchy distribution based on maximum likelihood estimators

Abstract: SUMMARY Tables, based on maximum likelihood estimators, are presented which enable one to obtain confidence intervals and test hypotheses about parameters of the Cauchy distribution. The difficulty in obtaining the maximum likelihood estimates of the parameters is discussed. Comparisons between the maximum likelihood estimators and the best linear unbiased estimators are presented.

On the maximum likelihood method of identification

Abstract: The maximum likelihood principle of estimation applied to the linear black-box identification problem gives models with theoretically attractive properties. Also, the method has been applied to industrial data (various processes in paper production) and proved able to work in practice.This paper presents further developments of the method in the case of a single output. The reliability and speed of the identification algorithm have been improved, and the method has been made easier to use. A rather sophisticated computer program, however, was needed. It employs a generalized model structure, an improved hill-climbing algorithm, and an automatic procedure for determining model orders and transport delays. Some statistics from performance tests of the program are presented.

Statistical methods for a general theory of all-or-none learning

Abstract: Greeno and Steiner have shown that a three state Markov Chain with a single absorbing state is equivalent to many of the current formalizations of All-or-None learning theories. Distribution statistics and other summary statistics are derived from the general model. Expressions for the maximum likelihood estimators of its parameters and the sampling variances of the estimates are presented. Likelihood ratio tests for several different null hypotheses are derived. These tests permit one to evaluate the usual null hypotheses in terms of the parameters of a process model.

Some Applications of the Maximum Likelihood Method in Seismology

Abstract: Summary The standard procedure of maximum likelihood estimation is stated. This procedure is applied to derive maximum likelihood estimators in some seismological problems, namely amplitude and phase corrections, group and phase velocities of surface waves and derivatives of traveltime curves dt/dA. The formulas for confidence regions for these functions are obtained.