Computing That Serves

Probability in a Certain World


Thursday, April 7, 2005 - 11:00am


Dennis Tolley, Department of Statistics, Brigham Young University

Since the mid 1920’s scientists have accepted that fact that there is an inherent uncertainty at the small particle level.  Using this uncertainty as a driving force, diffusion, entropy and general concepts of uncertainty have been derived as a motivation for the use of probability models.  Other scholars have used non-linear, irreversible processes such as processes far from equilibrium or chaotic processes, as models for generating apparent uncertainty.  In this presentation we will discuss a model for uncertainty based on the assumption that we live in a certain world.  First the fundamentals of probability and random variables are reviewed and illustrated.  An intrinsic data model is then derived when random variables have a joint probability distribution.  A method of marginalizing in a certain world is presented that yields the basic probability axioms of Kolmogorov from which a measure theoretic definition of probability can be derived.  More importantly, however, the intrinsic data model yields a method of using the constraints of the observer to generate a likelihood model.  Since likelihood is at the core of both Baysian and classical MLE methods, this model presents a unified method of using empirical evidence to build predictive models.


Dennis Tolley received his PhD. in biostatistics from the University of North Carolina in 1974 and his actuarial certification in 1981.  Since that time Tolley has been on the faculty of Duke University, TexasA&M University and is currently at Brigham Young University.  He has worked for the Japanese Ministry of Health in Hiroshima, Japan and Pacific Northwest Labs in Richland, Washington.  He has also worked with colleagues at the World Health Organization in Geneva, Switzerland, the World Bank in China and Chile, the Asian Development Bank in the Philippines and several private and government organizations in the U.S.  Projects include health care modeling, parasitic disease detection, exploration of coal, radiation effects on health, development of controllers, and bridging fundamental thermodynamic principles.

Currently, Tolley’s work entails two major areas of focus.  First is in the analysis of actuarial and health care cost data.  He is currently involved in developing macro health economics models from micro level data using statistical mechanics techniques.  He is also active in analytic chemistry, working on the development of tools for separation of proteins and for detection of biological and chemical agents.  Both areas of focus entail examination of the fundamentals of probability.