Course Goals and Approach
The goal of this course is to give an overview of fundamental ideas and
results about rational decision making under uncertainty, highlighting
the implications of these results for statistical practice. Rational
decision making has been a chief area of investigation in a number of
disciplines, in some cases for centuries. Several of the contributions
and viewpoints are relevant to both the education of a statistician and
to the development of sound statistical practices. Because of the
wealth of important ideas, this course in decision theory aims for
breadth rather than technical depth. It tries to bridge the gap among
the different fields that have contributed to rational decision making,
and presenting ideas in a unified framework while respecting and
highlighting the different and sometimes conflicting perspectives.
The spirit of the course is that of a ``guided tour'' of some of the
ideas and papers that have contributed to making decision theory so
fascinating and important. I selected a set of exciting papers and book
chapters, and developed a self contained lecture around each one.
Naturally, many wonderful articles have been left out of the tour. My
goal was to select a set that would work well in conveying an overall
view of the fields and controversies, rather than to select `greatest
hits'.
I will cover three areas: the axiomatic foundations of decision
theory; statistical decision theory; and optimal
design of experiments. At many universities, these are the subject of
separate courses, often taught in different departments and schools.
Current curricula in statistics and biostatistics are increasingly
emphasizing interdisciplinary training, reflecting similar trends in
research. Our plan reflects this need.
I designed our tour of decision theoretic ideas so that a student might
emerge with an overall philosophy of decision making and its
implications for the foundations of statistics. Ideally that philosophy
will be the students' own, and will be the result of contact with some
of the key ideas and controversies. I will attempt to put contributions of
each article in some perspective and to highlight developments that
followed. I will also use a consistent unified notation for the
entire material and emphasize the relationships
among different disciplines and points of view. But while most lectures
include current day materials, methods and results, all try to preserve
the viewpoint and flavor of the original contributions.
With very few exceptions, the mathematical level of the course is
intermediate and will require no measure theory. Advanced calculus and
intermediate statistical inference are very useful prerequisites, but an
enterprising student can profit from much of the course even without
this background. The most challenging aspect of the course lies in the swift
pace at which each lecture introduces new and different concepts and
points of view.