Stimulus sampling theory was developed in 1950s¹⁾ by American psychologist William Estes²⁾ influenced by works of Edwin Gurthie and his contiguity theory and one trial learning.³⁾ Estes' theory suggests that a particular stimulus-response association is learned in a single trial, but the overall learning process consists of accumulated S-R associations.

Stimulus sampling theory is also called a statistical learning theory, since its main aspect is the probability of a certain stimulus occurring in a trial and of being paired with a given response. According to this theory, a stimulus consists of one or more unobservable units, stimulus elements.⁴⁾ These elements are paired with various responses during the process of learning. The probability of a given response to a stimulus is equal to the number of stimulus elements associated with that response present in the given stimulus divided by the total number of stimulus elements associated with that response.

This theory is based mainly on five primitive notions⁵⁾:

• S - set of stimuli which is not directly observable
• r - number of responses
• t - number of possible trial outcomes
• X - sample space set containing all possibler experiments or trial sequences
• P - probability measure on the Borel field B(x) of cylinder sets of X⁶⁾

This basic variables form a broad set of axioms and formulas. Details can be found here.

Like all behaviorists, Estes viewed learning and behavior simply as mechanical. Still, later he included memory as a factor in his theory, and suggested stimuli don't directly cause a response. They evoke memories of previous experiences, enabling one to analyze possible outcomes and decide on the response that will lead to the most desirable outcome (scanning model of decision making).⁷⁾

Just like Gurthie, Estes rejected reinforcement and its relations to learning. Reinforcement has to do with the performance as it influences not learning, but rather how already learned material will manifest itself. Forgetting in Estes' theory occurred through unavailable stimulus elements due to external or internal variations. Spontaneous recovery can occur due to a relevant stimuli reoccurring.

Mathematical models of Estates and other behaviorists have helped in making psychological approach more scientific, yet this models have rarely introduced any new important concepts and were generally still considered too simple to explain all properties of learning.

• stimulus sampling theory, statistical learning
• William Estates

Estes, W. K., and Patrick Suppes. Foundations of Stimulus Sampling Theory. In Contemporary Developments in mathematical Psychology, 1:163-183. San Francisco: Freeman, 1974.

Kearsley, G. Stimulus Sampling Theory (W. Estes). The Theory Into Practice Database. Retrieved August 30th, 2011.

Cooper, S. Theories of Learning in Educational Psychology: Stimulus Sampling Theory. Retrieved August 30th, 2011.

Atkinson, Richard C., and William K. Estes. Stimulus sampling theory. In Handbook of mathematical psychology, 1963.

Estes, W.K. Toward a statistical theory of learning. Psychological Review, 57, 94-107. 1950.

Estes, W.K. Learning Theory and Mental Development. New York: Academic Press. 1970.