Reasoning to a Foregone Conclusion
JOSEPH B. KADANE
Statistics, Carnegie Mellon University
When can a Bayesian select an hypothesis H and design an experiment (or a
sequence of experiments) to make certain that, given the experimental
outcome(s), the posterior probability of H will be greater than its prior
probability? We discuss an elementary result that establishes sufficient
conditions under which this reasoning to a foregone conclusion cannot
occur. We illustrate how when the sufficient conditions fail, because
probability is finitely but not countably additive, it may be that a
Bayesian can design an experiment to lead his/her posterior probability
into a foregone conclusion. The problem has a decision theoretic version in
which a Bayesian might rationally pay not to see the outcome of certain
cost-free experiments, which we discuss from several perspectives. Also, we
relate this issue in Bayesian hypothesis testing to various concerns about
``optional stopping".
This is the joint work with
Mark J. SCHERVISH, and Teddy SEIDENFELD.
Refreshments: 3:30 - 4:00 p.m. Friday, at 327 Yost
Talk: 4:00 - 5:00 p.m. Friday, at 327 Yost.
Questions? jiayang@sun.cwru.edu
Wed Aug 13 13:54:29 EDT 1997