Paper Info
Title
The role of coherence in eliciting and handling imprecise probabilities and its application to medical diagnosis
Abstract
We refer to an arbitrary family H = {H-1,H-2,...,H-n} of events (hypotheses), i.e.,H has neither any particular algebraic structure nor is a partition of the certain event Omega. We detect logical relations among the given events (the latter could represent some possible diseases), and some further information is carried by probability assessments, relative to an event E (e.g., a symptom) conditionally to some of the H-t's ("partial likelihood"). If we assess (prior) probabilities for the events Hi's, then the ensuing problems are: (i) is this assessment coherent? (ii) is the partial likelihood coherent "per se"? (iii) is the global assignment (the initial one together with the likelihood) coherent? If the relevant answers are all YES, then we may try to "update" (coherently) the priors P(H-i) into the posteriors P(H,IE). This is an instance of a more general issue, the problem of coherent extensions: a very particular case is Bayes' updating for exhaustive and mutually exclusive hypotheses, in which this extension is unique. In the general case the lack of uniqueness gives rise to upper and lower updated probabilities, and we could now update again the latter, given a new event P and a corresponding (possibly partial) likelihood. In this paper, many relevant features of this problem are discussed, keeping an eye on the distinction between semantic and syntactic aspects. (C) 2000 Elsevier Science Inc. All rights reserved.
Year
DOI
Venue
2000
10.1016/S0020-0255(00)00085-2
Inf. Sci.
Keywords
Field
DocType
imprecise probability,medical diagnosis,decision analysis
Discrete mathematics,Uniqueness,Algebraic structure,Upper and lower probabilities,Coherence (physics),Artificial intelligence,Partition (number theory),Prior probability,Syntax,Mathematics,Machine learning,Bayes' theorem
Journal
Volume
Issue
ISSN
130
1-4
0020-0255
Citations 
PageRank 
References 
26
1.94
5
Authors
2
Name
Order
Citations
PageRank
Giulianella Coletti157271.49
Romano Scozzafava236748.05