Modelling Probabilistic and Logical Relations with Belief Functions.
Abstract
The project aims to explore through a variety of implementations a paradigm for the analysis of scientific and operational phenomena that depend on formalizations of uncertainty through probabilistic models. Such models can be interpreted as representations of random processes, or they can be interpreted as representations of the uncertainty of an analyst facing a situation described by the model. These interpretations are often viewed as mutually exclusive, but we regard them as complementary, and hence simultaneously applicable. A major motivating reason for constructing the models is to facilitate making uncertain inferences, followed in many cases by decision making informed by the inferences. The central principle of probabilistic inference remains, as it has been for 200 years, the Bayesian principle of updating inferences by formal computation of conditional probabilities, that is, by conditioning on the stream of incoming data. The belief function principle is a relaxation of the Bayesian rule, first suggested in special cases by R. A. Fisher about 65 years ago under the name fiducial inference, that retains the feature of conditioning on the data but does not require the full specification of a priori probabilities for all eventualities represented by the model. For example, in the ubiquitous class of Gaussian linear models the Bayesian formulation relies on awkward "improper priors" that are artifacts, that is, do not specify meaningful uncertainty judgments, whereas the normal linear belief function model dispenses with such priors and proceeds directly to conditioning.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 29, 1995
- Accession Number
- ADA300015
Entities
People
- Arthur P. Dempster
Organizations
- Harvard University