Advertisement

Psychometrika

, Volume 31, Issue 3, pp 383–395 | Cite as

Theorems for a finite sequence from a two-state, first-order markov chain with stationary transition probabilities

  • Richard S. Bogartz
Article

Abstract

Various theorems are obtained forN-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.

Keywords

Stationary Transition Markov Chain Public Policy Statistical Theory Binary Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Anderson, T. W. and Goodman, L. A. Statistical inference about Markov chains.Ann. math. Statist., 1957,28, 89–110.Google Scholar
  2. [2]
    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
  3. [3]
    Bower, G. H. Application of a model to paired-associate learning.Psychometrika, 1961,26, 255–280.Google Scholar
  4. [4]
    Brunk, H. D. On the estimation of parameters restricted by inequalities.Ann. math. Statist., 1958,29, 437–454.Google Scholar
  5. [5]
    Bush, R. R. Sequential properties of linear models. In R. R. Bush and W. K. Estes (Eds.),Studies in mathematical learning theory. Stanford: Stanford Univ. Press, 1959. Pp. 215–227.Google Scholar
  6. [6]
    Bush, R. R. Estimation and evaluation. In R. D. Luce, R. R. Bush, and E. Galanter (Eds.),Handbook of mathematical psychology, Vol. 1, New York: Wiley, 1963. Pp. 429–469.Google Scholar
  7. [7]
    R. D. Luce, R. R. Bush, and E. Galanter (Eds.),Readings in mathematical psychology, Vol. 1, New York: Wiley, 1963.Google Scholar
  8. [8]
    Miller, G. A. Finite Markov processes in psychology.Psychometrika, 1952,17, 149–167.Google Scholar
  9. [9]
    Sternberg, S. A path-dependent linear model. In R. R. Bush and W. K. Estes, (Eds.),Studies in mathematical learning theory. Stanford: Stanford Univ. Press, 1959. Pp. 308–339.Google Scholar
  10. [10]
    Suppes, P. and Atkinson, R. C.Markov learning models for multiperson interactions. Stanford: Stanford Univ. Press, 1960.Google Scholar

Copyright information

© Psychometric Society 1966

Authors and Affiliations

  • Richard S. Bogartz
    • 1
  1. 1.University of IowaUSA

Personalised recommendations