Bayesian Estimation and Classification
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.
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- Andergerg M.R. (1973), Cluster Analysis for Applications, Academic Press, New York.Google Scholar
- Abramson, N. (1963), Information Theory and Coding, McGraw Hill, New York.Google Scholar
- Bayes T. (1763) An Essay Towards Solving a Problem in the Doctrine of Changes, Philosophical Transactions of the Royal Society of London, Vol. 53, pages 370–418. and reprinted in 1958 in Biometrika Vol.45, pages 293–315.Google Scholar
- Cramer H. (1974), Mathematical Methods of Statistics. Princeton University Press, New Jersey.Google Scholar
- Fisher R. A. (1922), On the Mathematical Foundations of the Theoretical Statistics, Phil Trans. Royal. Soc. London, Vol. 222, Pages 309–368.Google Scholar
- Gersho A. (1982), On the Structure of Vector Quantisers, IEEE Trans. Information Theory, Vol. IT-28, pages 157–166.Google Scholar
- Gray R.M. (1984), Vector Quantisation, IEEE ASSP Magazine pages 4–29.Google Scholar
- Gray R.M., Karnin E.D, Multiple local Optima in Vector Quantisers, IEEE Trans. Information Theory, Vol. IT-28, pages 256–261.Google Scholar
- Jeffrey H. (1961), Scientific Inference, 3rd ed. Cambridge University Press.Google Scholar
- Larson H.J and Bruno O.S. (1979), Probabilistic Models in Engineering Sciences, Vol. I and II. Wiley, New York.Google Scholar