**An Additive Theory of Bayesian Evidence Accrual**

**Local PDF:** ADA364591.pdf

AD Number: ADA364591

Subject Categories: STATISTICS AND PROBABILITY

Corporate Author: LOS ALAMOS NATIONAL LAB NM ANALYSIS AND ASSESSMENT DIV

Title: An Additive Theory of Bayesian Evidence Accrual

Personal Authors: Winter, C. L.; Stein, Michael C.

Report Date: 1987

Pages: 43 PAGES

Report Number: LA-UR-93-3336

Contract Number: W-7405-ENG-36

Monitor Acronym: XF

Monitor Series: DOE

Descriptors: *BAYES THEOREM, PROBABILITY DISTRIBUTION FUNCTIONS, RANDOM
VARIABLES, APPROXIMATION(MATHEMATICS), DATA FUSION, APPLIED MATHEMATICS.

Abstract: We derive **a** theory of data fusion based on an additive approach to
Bayesian evidence combination and accrual. Although the additive method can be
stated in terms of simple formulae of probability, it is surprisingly rich. It
is robust against errors in data, and analysis and numerical simulations
indicate that estimated probabilities of hypotheses converge to the expected
value of **a** multiplicative Bayesian update as evidence that is mostly (but not
necessarily entirely) correct is accrued. We summarize the method and principal
results in the first part of the paper. The method relies on **a** representation
theorem for expected values of uncertain probabilities that is an extension of **a**
theorem of deFinetti's (deFinetti, 1937). The extension states that the expected
value of **a** function of uncertain probabilities can be represented as **a** weighted
sum of exchangeable random variables. We use the extended theorem to show that
the additive method approximates the expected value of the ordinary Bayesian
posterior, and they are equal in the limit. In the second part of the paper, we
sketch proofs of our theorems, derive the additive rule and contrast the
additive approach with others, especially multiplicative Bayesian updating on
one hand and various consensus-based rules on the other. We show that the
additive approach is much less sensitive to anomalous data than is Bayesian
updating. The additive method, while similar in spirit to consensus approaches,
is not ad hoc.

Limitation Code: APPROVED FOR PUBLIC RELEASE

Source Code: 415269

Citation Creation Date: 30 JUN 1999