combining estimators

[Robert Jacobs]

I have written a review article on statistical methods for
combining estimators.  Linear combination techniques are
covered, as well as supra Bayesian procedures.  The article
is scheduled to appear in the journal "Neural Computation"
(volume 7, number 5).  I recently received the page proofs
so I imagine that it will appear relatively soon, possibly
in the next issue.

I will put the abstract to the article at the bottom of this note.

Robbie Jacobs

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    Methods For Combining Experts' Probability Assessments

 This article reviews statistical techniques for combining
 multiple probability distributions.  The framework is that
 of a decision maker who consults several experts regarding
 some events.  The experts express their opinions in the form
 of probability distributions.  The decision maker must aggregate
 the experts' distributions into a single distribution that can
 be used for decision making.  Two classes of aggregation
 methods are reviewed.  When using a supra Bayesian procedure,
 the decision maker treats the expert opinions as data that
 may be combined with its own prior distribution via Bayes' rule.
 When using a linear opinion pool, the decision maker forms a
 linear combination of the expert opinions.  The major feature
 that makes the aggregation of expert opinions difficult is the
 high correlation or dependence that typically occurs among
 these opinions.  A theme of this paper is the need for training
 procedures that result in experts with relatively independent
 opinions or for aggregation methods that implicitly or explicitly
 model the dependence among the experts.  Analyses are presented
 that show that $m$ dependent experts are worth the same as $k$
 independent experts where $k \leq m$.  In some cases, an exact
 value for $k$ can be given; in other cases, lower and upper bounds
 can be placed on $k$.