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Markov Processes in Learning Theory

Published online by Cambridge University Press:  01 January 2025

John G. Kemeny  and
J. Laurie Snell
John G. Kemeny
Affiliation:
Dartmouth College
J. Laurie Snell
Affiliation:
Dartmouth College
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Abstract

Consideration is given mathematical problems arising in two learning theories—one developed by Bush and Mosteller, the other developed by Estes. The theory of Bush and Mosteller leads to a class of Markov processes which have been studied in considerable detail (see [1] and [7]). The Estes model can be treated as a Markov chain, i.e., a Markov process with a finite number of states. For an important class of special cases, it is shown that the Bush-Mosteller model is, in a sense, a limiting form of the Estes model. The limiting probability distributions are derived for the cases treated in both models.

Type
Original Paper
Information
Psychometrika , Volume 22 , Issue 3 , September 1957 , pp. 221 - 230
Copyright
Copyright © 1957 The Psychometric Society

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Footnotes

*

This research was supported by the National Science Foundation through a grant given to the Dartmouth Mathematics Project.

References

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