Association for Behavior Analysis International

The Association for Behavior Analysis International® (ABAI) is a nonprofit membership organization with the mission to contribute to the well-being of society by developing, enhancing, and supporting the growth and vitality of the science of behavior analysis through research, education, and practice.

SQAB Tutorial: What Is MPR and How Has It Evolved?

Peter Killeen (Arizona State University)

Invited Tutorial



Biography:Peter received his doctorate in 1969 under the perplexed gazes of Howie Rachlin, Dick Herrnstein, and Fred Skinner. His only position was at Arizona State University (arriving as the department Previously-Known-As Fort Skinner in the Desert fell to the nativists). He has studied choice behavior, schedule-induced responses like polydipsia, reinforcement schedules, interval timing, and delay discounting. His reinforcers include the Poetry in Science Award; the APA Div. 25 Med Outstanding Researcher Award; the Hilgard Award for the Best Theoretical Paper on Hypnosis (!); the F. J. McGuigan Lecture on Understanding the Human Mind (!!); Presidents of the Society of Experimental Psychologists, the Society for the Quantitative Analysis of Behavior, and the 3rd International Seminar on Behavior (SINCA). A year at the Institute for Advanced Studies in Oslo birthed a behavioral energetics theory of ADHD, which received The Faculty of 1000’s “Must Read”. His statistic prep was an Emerging Research Front Feature on Thomson Reuters Sciencewatch. He has written oodles of screeds on choice and on timing; his first, now receiving social security, showed that pigeons were indifferent between free food and schedules where they had to work for it; his latest is a deep dive into the perception of sequential stimuli in the context of timing. He has also urged our field to turn some of their efforts to understanding the role of emotions in behavior, and to bridging to the field at large through study embodied cognition. In his golden years, family and friends; the health of behavior analysis; admiring nature; and thinking deep thoughts, are foremost in his life.



Galileo’s “book of nature is written in the language of mathematics.” What are the mathematical sentences for reinforcement schedules? Good theories are based on principles, or axioms, so you know what they assume. Those in the Mathematical Principles of Reinforcement (MPR) are: Reinforcers: 1) excite, and 2) direct, responding, which 3) takes time. Baum’s and Catania’s theories have similar principles. I describe the data that motivate each principle, and the mathematics that animate those principles and their interactions. Each of the principle-models were specific enough to be tested, and to evolve into more precise, or more general ones. The first, for example, is A = ar, where A is activation, a motivation, and r rate of reinforcement. I describe two of the basic schedules to give a sense of the machinery; and then note its extension to adjunctive behaviors, contrast, progressive ratio schedules, and behavioral momentum theory. I show data that required refinement of the models. Finally I shall relate MPR to a recent general theory of time perception, and bridge that to Shahan and Gallistel’s information theoretic approach to reinforcement, sketching the blueprint of a grand theory of perception and action


Modifed by Eddie Soh