Since World War II, most mathematicians have favored treating probability theory as a branch of measure theory. This reliance on measure theory tells us nothing about how to use mathematical probability, leaving statisticians and philosophers free to debate whether it is subjective (degree of belief) or objective (frequency or propensity). The game-theoretic foundation for probability, recently shown to be a viable alternative to the measure-theoretical foundation (www.probabilityandfinance.com), gives more philosophical guidance. It tells us that probabilistic theories should be understood as making predictions: they predict particular events by giving them very high probability. Whether these predictions are subjective (we believe the events will happen) or objective (we claim they really will happen) is often only a nuance. More important than this nuance is the setting in which predictions are made. (1) When a probabilistic theory successfully predicts a long sequence of future events (as quantum mechanics does), it tells us something about phenomena. (2) When a probabilistic theory predicts only one step at a time (basing each successive prediction on what happened previously), it has practical value but tells us nothing about phenomena; we can say this because the method of defensive forecasting has been shown to succeed in this setting (pass statistical tests) regardless of how events come out. (3) When we talk about the probability of an isolated event, which different people can place in different sequences, we are weighing arguments, and our predictions are only as good as our arguments; this is the place of evidence theory.
Glenn Shafer spent his childhood on a farm near Cany, Kansas. He earned an undergraduate degree in mathematics from Princeton in 1968, and after a stint in the Peace Corps in Afghanistan, he earned a doctoral degree in mathematical statistics from Princeton in 1973. After teaching at Princeton and the University of Kansas, he came to Rutgers Business School in 1992. He is best known for launching the Dempster-Shafer theory with his 1976 book A Mathematical Theory of Evidence.
**refreshments will be served at 3:30 pm**
Talk will be broadcast live on RU-TV
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