Probability and Statistics: Some Thoughts
on the Basic Course Sequence
Arthur Dempster
Harvard University
What should be the objectives and contents of a future-oriented
year-long course assuming a middling calculus and linear algebra
prerequisite? I argue that current topics for science and engineering
students must surely include: (1) reconciliation of probabilities as
long-run frequencies AND as quantifications of specific scientific
uncertainties, (2) understanding of both S-inference based on prior
stochastic assumptions AND P-inference based on Bayes posterior
uncertainties as having different but comparably important logical contents
and practical roles, and (3) recognition of decision analysis as a tool
that illuminates significance tests and other S-inference tools via
Neyman-Pearson theory (Have we achieved "proven" detection that global
warming is real?) AND in a very different and fundamental way supports
real-world decisions based on P-inference (Do we need "prudent" action
to forestall the possible effects of global warming?). These principles
suggest that we need a radical restructuring of the contents of current
standard offerings. In particular, Bayes deserves equal billing because
computing technology has facilitated Bayesian answers to important
questions about complex phenomena.
Back to statistics seminar home page