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Derivations of Learning Statistics from Absorbing Markov Chains

Published online by Cambridge University Press:  01 January 2025

Richard B. Millward
Richard B. Millward*
Affiliation:
Brown University
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Abstract

Learning-process statistics for absorbing Markov-chain models are developed by using matrix methods exclusively. The paper extends earlier work by Bernbach by deriving the distribution of the total number of errors, u-tuples, autocorrelation of errors, sequential statistics, and the expectation and variance of all statistics presented. The technique is then extended to latency derivations including the latencies of sequential statistics. Suggestions are made for using the sequential-statistic algorithm in a maximum-likelihood estimation procedure. The technique is important because statistics for very large absorbing matrices can be easily computed without going through tedious theoretical calculations to find explicit mathematical expressions.

Type
Original Paper
Information
Psychometrika , Volume 34 , Issue 2 , June 1969 , pp. 215 - 232
Copyright
Copyright © 1969 The Psychometric Society

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Footnotes

*

The author is indebted to his students Thomas Wiekens and Richard Freund who were helpful in the development of this paper. Support was received for this work from Grant MH-11255 from the National Institutes of Mental Health.

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