34 research outputs found
Quasi-Bayesian Analysis Using Imprecise Probability Assessments And The Generalized Bayesâ Rule
The generalized Bayesâ rule (GBR) can be used to conduct âquasi-Bayesianâ analyses when prior beliefs are represented by imprecise probability models. We describe a procedure for deriving coherent imprecise probability models when the event space consists of a finite set of mutually exclusive and exhaustive events. The procedure is based on Walleyâs theory of upper and lower prevision and employs simple linear programming models. We then describe how these models can be updated using Cozmanâs linear programming formulation of the GBR. Examples are provided to demonstrate how the GBR can be applied in practice. These examples also illustrate the effects of prior imprecision and prior-data conflict on the precision of the posterior probability distribution. Copyright Springer 2005imprecise probability, generalized Bayesâ rule, second-order probability, quasi-Bayesian analysis,