Bayesian Estimation and Classification
Saeed V. Vaseghi · 1996
Bayesian estimation is a framework for formulation of statistical inference problems, and includes the classical estimators such as the maximum a posterior, maximum likelihood, minimum mean squared error, and minimum mean absolute value of error as its special cases. The hidden Markov model, widely used in statistical signal processing, is also an example of a Bayesian model. Bayesian inference is based on the minimisation of a so called Bayes risk function which includes; a posterior model of the unknown parameters given the observation, and a cost of error function. This chapter begins with an introduction to the basic concepts of estimation theory, and considers the statistical measures that are used to quantify the performance of an estimator. We study the Bayesian estimation methods and consider the effects of using a prior model on the mean and the variance of an estimate. Estimation of discrete-valued parameters, and parameters from a finite-state process, are studied within the frame work of Bayesian classification. The chapter concludes with a study of the methods for the modelling of a random signal space.