Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T17:26:56.580Z Has data issue: false hasContentIssue false
  • English
  • Français

The recursive estimation of a Markov chain

Published online by Cambridge University Press:  14 July 2016

B. J. N. Blight  and
J. L. Devore
B. J. N. Blight
Affiliation:
Birkbeck College, University of London
J. L. Devore
Affiliation:
Oberlin College, Oberlin, Ohio
Get access Rights & Permissions [Opens in a new window]

Abstract

For every hth member of a two-state Markov chain the value of a random variable Y is observed where the distribution of Y is conditional on the state of the corresponding member of the chain. A recursive set of equations is derived giving the posterior probabilities for both the observed and unobserved members. The use of this recursive solution to investigate the optimality of certain simple classification rules is discussed, and a “classification by runs” is also presented.

Keywords

MARKOV CHAINRECURSIVE ESTIMATIONBINOMIAL SAMPLINGNAIVE ESTIMATION RULE
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 394 - 400
Copyright
Copyright © Applied Probability Trust 1974 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bather, J. A. (1963) Control charts and the minimization of costs. J. R. Statist. Soc. B 25, 49–70.Google Scholar
Broadbent, S. R. (1958) The inspection of a Markov process. J. R. Statist. Soc. B 20, 111–119.Google Scholar
Campling, G. E. G. (1968) Serial sampling inspection for large batches of items where the mean quality has a normal prior distribution. Biometrika 55, 393–399.Google Scholar
Cox, D. R. (1960) Serial sampling acceptance schemes derived from Bayes' theorem. Technometrics 2, 353–360.Google Scholar
Devore, J. L. (1973) The naive rule for reconstructing a noisy Markov chain. Biometrika 6, 227–234.Google Scholar
Holt, C.C. (1957) Forecasting seasonals and trends by exponentially weighted moving averages. O. N. R. Memorandum No. 52, (Carnegie Institute of Technology).Google Scholar
Preston, P. E. (1971) An empirical Bayes problem with a Markovian parameter. Biometrika 58, 535–544.Google Scholar
Switzer, P. (1971) Mapping a geographically correlated environment. Proceedings of the International Symposium on Statistical Ecology, Yale University. Volume l, 235–270.Google Scholar