Morris Herman DeGroot (1931–1989) was an American statistician whose elegant textbook Optimal Statistical Decisions (1970) provided a generation of students with a rigorous and accessible introduction to Bayesian decision theory. A professor at Carnegie Mellon University for most of his career, DeGroot also made important contributions to the theory of consensus, the calibration of probability assessors, and the foundations of Bayesian inference. He was instrumental in building Carnegie Mellon's Department of Statistics into one of the world's leading centers of Bayesian research.
Early Life and Education
DeGroot was born in 1931 and received his PhD from the University of Chicago in 1958, where he was influenced by the strong Bayesian tradition associated with Savage. He joined Carnegie Mellon University (then Carnegie Institute of Technology) in 1957, where he remained for the rest of his career. He played a central role in shaping the department and mentoring the next generation of Bayesian statisticians.
Optimal Statistical Decisions
DeGroot's masterwork, Optimal Statistical Decisions, published in 1970, was a lucid and comprehensive treatment of Bayesian decision theory. It covered utility theory, subjective probability, prior distributions, Bayesian estimation, hypothesis testing, sequential analysis, and optimal design of experiments, all within a unified Bayesian framework. The book was notable for its mathematical rigor combined with clear exposition, and it became a standard graduate text in statistics departments worldwide.
DeGroot helped establish Carnegie Mellon as a powerhouse of Bayesian statistics. The department's emphasis on decision theory, subjective probability, and applied Bayesian methods attracted leading researchers and produced influential graduates. This tradition continues today, with Carnegie Mellon remaining one of the most important centers for Bayesian computation and theory.
Consensus and Combining Opinions
DeGroot made significant contributions to the problem of combining the probability judgments of multiple experts. His 1974 paper “Reaching a Consensus” proposed a model in which experts iteratively revise their probability assessments based on a weighted average of others' opinions, with weights reflecting how much each expert trusts the others. This model has been widely applied in group decision-making and forecasting.
Calibration
DeGroot also contributed to the study of calibration—the question of whether a probability assessor's stated probabilities match the actual frequencies of events. A well-calibrated forecaster who says “70% chance of rain” should see rain about 70% of the time such a forecast is made. DeGroot's work on calibration scoring rules helped formalize how to evaluate and compare subjective probability assessments.
“The optimal statistical decision is the one that maximizes expected utility with respect to the posterior distribution of the unknown parameters.”— Morris DeGroot, Optimal Statistical Decisions (1970)
Legacy
DeGroot died of cancer in 1989 at the age of fifty-eight. His contributions extended beyond research to an extraordinary gift for exposition and mentorship. In addition to Optimal Statistical Decisions, he co-authored the popular undergraduate textbook Probability and Statistics (with Mark Schervish), which introduced Bayesian concepts to generations of students. The DeGroot Prize, awarded by the International Society for Bayesian Analysis, honors his memory.
Born in the United States.
Joined the faculty at Carnegie Mellon University.
Received PhD from the University of Chicago.
Published Optimal Statistical Decisions.
Published “Reaching a Consensus” on combining expert opinions.
Served as founding editor of Statistical Science.
Died on 2 November, aged fifty-eight.