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William Kaye Estes (born June 17, 1919 in Minneapolis, Minnesota) is an American psychologist.

Biographical information


He achieved his 1940 and his PhD in 1943 , both at University of Minnesota. As an undergraduate, he was a student of Richard M. Elliott. As a graduate student he stayed at the there and worked under B. F. Skinner. When he later had his doctorate, he joined Skinner on the faculty at Indiana University.


Estes first joined the Indiana University faculty in 1946 and reached the rank of Research Professor in 1960. In 1962, he moved to Stanford University, then in 1968 to Rockefeller University and in 1979 to Harvard University. He returned to Indiana 1999.

Main areas of interest

Estes's early research, involved animal learning and behavior. He worked with with B. F. Skinner. They presented their analysis of anxiety and introduced the Conditioned Emotional Response (CER) paradigm. In their CER paradigm, rats were trained to respond on an operant schedule that produced a steady response rate, after which they were tested with a stimulus that was conditioned as a fear signal. The fear signal suppressed the operant response, and the magnitude of suppression was used as a mesure of anxiety. The CER became widely used to study Pavlovian conditioning, in a variety of organisms.

He the took to studying visual information processing in the 1960's, contributing to the visual detection method of estimating the information apprehended from brief visual displays.

After Estes got out of the U. S. Army at the end of World War II, he established his reputation as one of the originators of mathematical learning theory. When high speed, high capacity computers later came along, Estes' models laid the foundation for modern artificial intelligence and artificial neural network developments. Estes went from Indiana University to Stanford University, to Rockefeller University in New York, and finally to Harvard University. After retiring from Harvard, he returned to Bloomington, Indiana, where he remained active in academics to become professor emeritus at his original academic home department.

One of William Estes's most famous contributions to learning theory was his model of intelligence, in which he postulated that the rate of change in a human's knowledge is equal to the product of their intelligence and the difference between their current level of knowledge and their studiousness. Mathematically, this can be expressed by the differential equation dk/dt+lk=λl, where knowledge k and studiousness λ are expressed as percentages, which has the solution k=λ(1-e^(-lt)), assuming that the human began with no knowledge of the subject. Taking the limit as time approaches infinity, one finds that, given an infinite amount of time, a human's knowledge is equal only to their studiousness; the intelligence l merely affects the rate at which his or her knowledge approaches that limit.

He developed Stimulus-sampling theory a mathematical approach to learning theory

In later years his research has focused on mathematical and computer modeling of human memory and classification learning. He is credited with being one of the founders of modern mathematical psychology


Estes was received a a large number of honours. They include

  • Being elected to the National Academy of Sciences in 1963
  • Being elected to American Academy of Arts and Sciences in 1982.
  • Distinguished Research Contribution Award of the American Psychological Association in 1962,
  • Warren Medal of the Society of Experimental Psychologists in 1963,
  • American Psychological Foundation Gold Medal for Lifetime Achievement in Psychological Science in 1992 and the
  • U. S. National Medal of Science in 1997.

Editorial board/consulting editor

Association affiliations

See also



Estes, W.K. (1994) - Classification and Cognition. Oxford University Press.

Estes, W.K. (1991) - Statistical models in behavioral research. Hillsdale, NJ: Erlbaum Associates

Book Chapters


Estes, W.K. (1997) - Processes of memory loss, recovery, and distortion. Psychological Review, 104, 148-169.


  • Bower, G H (1994), "A turning point in mathematical learning theory.", Psychological Review 101 (2): 290–300, 1994 Apr, doi:10.1037/0033-295X.101.2.290, PMID 8022959 
  • Estes, William K. (1989), Lindzey, Gardner, ed., A History of Psychology in Autobiography, Stanford University Press, pp. 94--125, ISBN 0804714924 

External links