On the use of a new discrepancy measure to correct incoherent assessments and to aggregate conflicting opinions based on imprecise conditional probabilities

We give a preliminary study of a new procedure to correct incoherent imprecise conditional probability assessments. The procedure is based on parametric optimization problems which have as objective function a new discrepancy measure. We show through simple examples how the procedure of correcting incoherent assessments can be properly extended to aggregate con∞icting opinions, and can be generalized to embed importance weights of each assessment.

[1]  Gert de Cooman,et al.  Coherent lower previsions in systems modelling: products and aggregation rules , 2004, Reliab. Eng. Syst. Saf..

[2]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[3]  Serafín Moral,et al.  Aggregation of Imprecise Probabilities , 1998 .

[4]  R. Scozzafava,et al.  Probabilistic Logic in a Coherent Setting , 2002 .

[5]  Susanne Rässler,et al.  Statistical Matching: "A Frequentist Theory, Practical Applications, And Alternative Bayesian Approaches" , 2002 .

[6]  L. Bregman.  The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming , 1967 .

[7]  Barbara Vantaggi,et al.  Statistical matching of multiple sources: A look through coherence , 2008, Int. J. Approx. Reason..

[8]  R. Cooke.  Experts in Uncertainty: Opinion and Subjective Probability in Science , 1991 .

[9]  Christian Genest,et al.  Combining Probability Distributions: A Critique and an Annotated Bibliography , 1986 .

[10]  P. Walley,et al.  Direct algorithms for checking consistency and making inferences from conditional probability assessments , 2004 .

[11]  Romano Scozzafava,et al.  The role of coherence in eliciting and handling imprecise probabilities and its application to medical diagnosis , 2000, Inf. Sci..

[12]  Minh Ha-Duong.  Hierarchical fusion of expert opinions in the Transferable Belief Model, application to climate sensitivity , 2008, Int. J. Approx. Reason..

[13]  Angelo Gilio.  Probabilistic relations among logically dependent conditional events , 1999, Soft Comput..

[14]  Robert Nau,et al.  The Aggregation of Imprecise Probabilities , 2002, ISIPTA.

[15]  Andrea Capotorti,et al.  Coherent correction of inconsistent conditional probability assessments , 2008 .

[16]  F. Lad.  Operational Subjective Statistical Methods: A Mathematical, Philosophical, and Historical Introduction , 1996 .