Teddy Seidenfeld

Working on the foundations of statistics, I enjoy thinking about problems that involve the vague notion of "ignorance." The question was alive for Thomas Bayes in 1760. Bayes' work stimulated Simon Laplace a decade later to argue that equiprobability was the key: he thought that where you are ignorant between two events, you should assign them equal probability. However, using this equiprobability rule to depict "ignorance" leads to some unanticipated results when there are infinitely many possibilities, as is typical of statistical problems with an unknown parameter. For a simple example, think of choosing a number x "at random." Formally, a uniform distribution for x corresponds to a finitely (but not countably) additive probability. Mark Schervish, Jay Kadane, and I have shown some very surprising consequences for statistical inference that attend the use of merely finitely additive probabilities. These surprises affect statistical decision theory.

Also I am interested in the general question of whether the norms of Bayesian statistics can be extended from individuals acting alone to cooperative groups. In terms of comparing opinions of different researchers, when will common evidence drive them to agree in their personal probabilities? In terms of decisions, when can two Bayesians acting in partnership make (coherent) decisions that preserve their common preferences? Jay Kadane, Mark Schervish and I have found that these two perspectives on groups (considering the agreements in probabilities versus the agreements in decision) lead to very different results. Our current work is aimed at providing a unified treatment of group probabilities and group decisions. The strategy we employ is to relax a central assumption of Bayesian, expected utility theory: the "ordering" postulate. Instead, in our theory we do not assume that you always can judge which of two events is more probable, and we do not assume that you always can judge which of two options is more preferred.

Relating to this relaxation of the traditional Bayesian paradigm, together with Larry Wasserman and Tim Herron, we explore some anomalous dynamical features of so-called "Robust Bayesian" theory. Specifically, we examine when new evidence from an experiment is certain to increase disagreements among different Bayesian experts who share the new data. We call this phenomenon, "Dilation."

Some Related Publications

Heron, T., Seidenfeld, T., and Wasserman, L. (in press). "Divisive Conditioning: further results on Dilation," Phil. Science.

Seidenfeld, T. , Schervish, M.J., and Kadane, J. (1995). "A Representation of Partially Ordered Preferences," Ann. Stat., 23, pp. 2168-2217.

Seidenfeld, T. and Wasserman. L. (1993). "Dilation for Sets of Probabilities," Ann. Stat., 21, pp. 1139-1154.

Seidenfeld, T. (1992). "R.A. Fisher's Fiducial Argument and Bayes' Theorem," Stat. Sci., 7, pp. 358-368.

Schervish, M.J. and Seidenfeld, T. (1990). "An approach to consensus and certainty with increasing evidence," Journal of Stat.istical Planning and Inference, 25, pp. 401-414.

Seidenfeld, T., Kadane, J.B., and Schervish, M.J. (1989). "On the shared preferences of two Bayesian decision makers," Journal of Philosophy, 86, 225-244.

Kadane, J.B., Schervish, M.J., and Seidenfeld, T. (1986). "Statistical implications of finitely additive probability," in Bayesian Inference andDecision Techniques, P.K. Goel and A. Zellner (eds.), North Holland: Amsterdam, pp. 59-76.