A THREE STATE MARKOV MODEL FOR LEARNING 马尔可夫学习模型的三种状态
by John Theios
TECHNICAL REPORT NO.· 40
September 22, 1961
PSYCHOLOGY SERIES
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INSTITUTE FOR· MATHEMATICAL STUDIES IN TRE SOCIAL SCIENCES
Applied Mathematics and Statistics Laboratories
STANFORD UNIVERSITY
Stanford, California
A THREE STATE MARKOV MODEL FOR LEARNINGY
John Theios
Stanford University
In many learning situations, the response under study initially haszero probability of occurring, but asymptotically, the response probability approaches unity. A few situations of this type are instrumentalavoidance conditioning, classical defense and appetitive conditioning,and reversal learning. These situations will be referred to as simpleconditioning (se). In the past, se has been analyzed in terms of responsestrength or linear operator models (Hull, 1943; Estes, 1950; Bush &Mosteller, 1955), which assume that the strength or probability of alearned response increases gradually during the Course of learning.Recently, it has been found that Markov models, which assume that learning takes place on single trials in an all-or-none fashion, more adequatelydescribe some types of verbal learning than do the linear models (Bower,1960; Estes, 1960). It is quite possible that se is also characterizedby some sort of discrete learning as opposed to gradual learning. Thispossibility is further enhanced by the fact that the "zero to.Unity"response probabilities, characteristic of se, should lend themselvesnicely to discrete conditioning states, which a Markov interpretationwould require (cf., Suppes &Atkinson, 1960). The present paper presentsI am indebted to Dr. Gordon H. Bower for deriving a: number of thetheoretical predictions and for his valuable interest and adviceduring the development of this paper.a three state absorbing Markov model for SC, and then compares thetheoretical predictions to actual data collected in an extensiveexperiment on avoidance conditioning of rats.
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