Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-29T12:38:01.104Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic properties of a certain class of Bush–Mosteller learning models

Published online by Cambridge University Press:  01 July 2016

Peter Findeisen
Peter Findeisen*
Affiliation:
University of Düsseldorf
*
∗Postal address: Psychologisches Institut der Universität Düsseldorf, Lehrstuhl für Psychologie IV, 4000 Düsseldorf, Universitätsstrasse 1, W. Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

One general and three specialized models of the Bush–Mosteller type are presented to describe the kind of learning experiment where the response of the learner is always reinforced. Inhomogeneity is admitted. The random sequences of response probabilities and of responses associated with the different models are considered. Information about the existence and the distribution of asymptotic response probabilities is provided. The stress is on sufficient and necessary conditions for convergence (a.s. or with positive probability) of the response sequence, which is what ‘learning' means.

Keywords

RANDOM SYSTEMS WITH COMPLETE CONNECTIONSLEARNING MODELSBUSH–MOSTELLER MODELS
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 4 , December 1980 , pp. 922 - 941
Copyright
Copyright © Applied Probability Trust 1980 

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

Bush, R. B. and Mosteller, F. (1955) Stochastic Models for Learning. Wiley, New York.CrossRefGoogle Scholar
Findeisen, P. (1978) Untersuchung einiger stochastischer Lernmodelle unter besonderer Beruecksichtigung von Modellen mit Wegabhaengigkeit. Dissertation, Universität Dortmund.Google Scholar
Iosifescu, M. and Theodorescu, R. (1969) Random Processes and Learning. Springer, Berlin.Google Scholar
Luce, R. D. (1959) Individual Choice Behavior. Wiley, New York.Google Scholar
Neveu, J. (1965) Mathematical Foundations of the Calculus of Probability. Holden-Day, San Francisco.Google Scholar
Norman, M. F. (1972) Markov Processes and Learning Models. Academic Press, New York.Google Scholar
Sternberg, S. (1963) Stochastic learning theory. Chapter 9 of Handbook of Mathematical Psychology , ed. Luce, R. D., Bush, R. B. and Galanter, E. Wiley, New York.Google Scholar