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Stochastic Learning Models

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Four kinds of studies of learning might reasonably be discussed under the title of this paper 1 mathematical research on the theory of neuron networks, 2 the design of self-organizing mechanisms such as robots or computing machines 16, 3 the parts of information and communication theory that fall in the field of statistical behavioristics 29, 4 stochastic learning models for simple psychological experiments. This paper deals with the fourth topic.There is a small but growing body of literature on statistical models constructed to assist experimental psychologists in the design, analysis, and explanation of some comparatively simple trial-by-trial learning experiments carried out under highly controlled conditions. In these experiments the response is either classified categorically or given as a time measure. Because these models emphasize both the step-by-step process of learning and its statistical features, problems of time dependence, statistical estimation, and occasionally problems in theoretical probability arise. Thus far, sufficiently little work both of an experimental and theoretical nature has been done on the models and their extensions that there is still considerable unity in the publications. Furthermore the notions involve dare quite elementary. In this brief discussion two general categories of mathematical learning models have been omitted. Thurstone 35 develops learning curves initially from an urn scheme, but turns from this probabilistic model to differential equations. Similarly Gulliksen 201and Gulliksen and Wolfle 21 and many others before and since work from differential equations, rather than from the kind of trial-by-trial models that are principally discussed below. On the other hand, Hulls extensive work for one example see 26 has been omitted, though it is sometimes related to the models presented here, because his postulational system would require a review of its own.

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  • Statistics and Probability

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