Variance of Bayes estimates

1 November 1971

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory

Vol. 17 (6) , 665-669
https://doi.org/10.1109/tit.1971.1054718

Abstract

This paper contains an analysis of the performance of Bayes conditional-mean parameter estimators. The main result is that on a finite parameter space such estimates exhibit a mean-square error that diminishes exponentially with the number of observations, the observations being assumed to be independent. Two situations are discussed: true parameter included in the parameter space and true parameter not included in the parameter space. In the former instance only very general assumptions are required to demonstrate the exponential convergence rate. In the latter case the existence of an information function must be invoked. Comments on the continuous-parameter-space realization of the estimator and a discussion of the convergence mechanism are also included.

Keywords

This publication has 8 references indexed in Scilit:

Quasi-Bayes averaging of stochastic approximation estimators
Information and Control, 1971
On unsupervised estimation algorithms
IEEE Transactions on Information Theory, 1970
Stochastic estimation of a mixture of normal density functions using an information criterion
IEEE Transactions on Information Theory, 1970
Unsupervised learning and the identification of finite mixtures
IEEE Transactions on Information Theory, 1970
Stochastic Approximation Algorithms for System Identification, Estimation, and Decomposition of Mixtures
IEEE Transactions on Systems Science and Cybernetics, 1969
On the Identifiability of Finite Mixtures
The Annals of Mathematical Statistics, 1968
Identifiability of Finite Mixtures
The Annals of Mathematical Statistics, 1963
Identifiability of Mixtures
The Annals of Mathematical Statistics, 1961