Relevance of the Bayesian paradigm for "applied probabilists"

This paper is based on an invited lecture given by the author at the ORSA/TIMS Special Interest Group on Applied Probability Conference on Statistical and Computational Problems in Probability Modeling, held at Williamsburg, Virginia, January 7-9, 1985. The theme of this paper is twofold. First, that members of the above group should be seriously concerned with issues of statistical inference - they should not stop short upon proposing a probability model. Second, that inference be undertaken via a strict adherence to the rules of probability - the Bayesian paradigm. To underscore a need for emphasizing the first theme, it may be pertinent to note that an overwhelming majority of the papers dealing with statistical and inferential issues that were presented at this conference were authored by members who did not claim to belong to the ORSA/TIMS Special Interest Group on Applied Probability. The lecture was followed by a panel discussion, with Drs. Lyle Broemeling and Edward Wegman of the Office of Naval Research as discussants. Dr. Robert Launer of the Army Research Office served as a moderator. Discussions from the floor included comments by Professors D. Harrington of Harvard University, E. Parzen of Texas A & M University, and R. Smith of Imperial College, London, England. This paper, and the comments of the panelists, are published in this volume of the Annals of Operations Research, which is going to serve as a Proceedings of the Conference. © 1987 J.C. Baltzer A.G., Scientific Publishing Company.