Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-07T18:16:57.238Z Has data issue: false hasContentIssue false
  • English
  • Français

Theorems for a Finite Sequence from a Two-State, First-Order Markov Chain with Stationary Transition Probabilities

Published online by Cambridge University Press:  01 January 2025

Richard S. Bogartz
Richard S. Bogartz*
Affiliation:
University of Iowa
Get access Rights & Permissions [Opens in a new window]

Abstract

Various theorems are obtained for N-trial sample sequences from the general two-state, first-order Markov chain with stationary transition probabilities. Four lemmas which facilitate the derivations are given. A brief discussion of applications to binary data, estimation, and evaluation is given, including a maximum-likelihood procedure for estimating transition probabilities which are restricted by inequalities.

Type
Original Paper
Information
Psychometrika , Volume 31 , Issue 3 , September 1966 , pp. 383 - 395
Copyright
Copyright © 1966 Psychometric Society

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

Anderson, T. W. and Goodman, L. A. Statistical inference about Markov chains. Ann. math. Statist., 1957, 28, 89–110.CrossRefGoogle Scholar
Bogartz, R. S. Extension of a theory of predictive behavior to immediate recall by preschool children. Paper read at the First Michigan Symposium on the Development of Language Functions. Ann Arbor, October, 1965.Google Scholar
Bower, G. H. Application of a model to paired-associate learning. Psychometrika, 1961, 26, 255–280.Google Scholar
Brunk, H. D. On the estimation of parameters restricted by inequalities. Ann. math. Statist., 1958, 29, 437–454.CrossRefGoogle Scholar
Bush, R. R. Sequential properties of linear models. In Bush, R. R. andEstes, W. K. (Eds.), Studies in mathematical learning theory. Stanford: Stanford Univ. Press, 1959, 215–227..Google Scholar
Bush, R. R. Estimation and evaluation. In Luce, R. D., Bush, R. R., and Galanter, E. (Eds.), Handbook of mathematical psychology, Vol. 1. New York: Wiley, 1963, 429–469..Google Scholar
Luce, R. D., Bush, R. R., andGalanter, E. Readings in mathematical psychology, Vol. 1, New York: Wiley, 1963.Google Scholar
Miller, G. A. Finite Markov processes in psychology. Psychometrika, 1952, 17, 149–167.CrossRefGoogle Scholar
Sternberg, S. A path-dependent linear model. In Bush, R. R. and Estes, W. K. (Eds.), Studies in mathematical learning theory. Stanford: Stanford Univ. Press, 1959, 308–339..Google Scholar
Suppes, P. and Atkinson, R. C.. Markov learning models for multiperson interactions, Stanford: Stanford Univ. Press, 1960.Google Scholar