I am pleased to announce the electronic availability of my dissertation
(postscript, 1.9MB, 140 pages) :
http://www.neci.nj.nec.com/homepages/dpennock/papers/thesis.ps
TITLE: Aggregating Probabilistic Beliefs: Market Mechanisms and
Graphical Representations
Ph.D. Dissertation, University of Michigan, 1999
David M. Pennock
ABSTRACT
A long-standing question in statistics is how best to aggregate the
probabilistic beliefs of multiple agents. Related is the practical
question of how to represent the combined beliefs efficiently. This
dissertation reports contributions on both fronts.
First, I formulate and analyze a securities market mechanism for
aggregating beliefs. Equilibrium prices in the market are interpreted as
consensus beliefs. Under homogeneity conditions regarding agents'
utilities, the market mechanism corresponds with standard aggregation
functions, and the market's outward behavior is indistinguishable from
that of a rational individual. I also explore extensions to the model in
which agents learn from prices and the market as a whole adapts over
time. In certain circumstances, price fluctuations can be viewed as the
Bayesian updates of an individual.
Second, I investigate the use of graphical models, and in particular
Bayesian networks, for representing aggregate beliefs. I derive two
impossibility theorems which contradict widely held intuitions about how
Bayesian networks should be combined. On a more positive note, the
so-called logarithmic opinion pool is shown to admit relatively concise
encodings. I describe the nature of graphical structures consistent with
this pooling function, and give algorithms for computing the logarithmic
and linear opinion pools with, in some cases, exponential speedups over
standard methods.
Finally, I apply and extend the graphical modeling results to the market
framework, deriving sufficient conditions for compact markets to be
operationally complete. Such markets still induce a complete consensus
distribution and support Pareto optimal allocations of risk, but with
exponentially fewer securities than required for traditional
completeness.
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My new coordinates are:
NEC Research Institute
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Princeton, NJ 08540
Office: (609) 951-2715
Fax: (609) 951-2488
Email: dpennock@research.nj.nec.com
URL: http://www.neci.nj.nec.com/homepages/dpennock
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