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It is with great pleasure that I welcome this collection of diverse and stimulating contributions to the Dempster-Shafer theory of belief functions. This paper has two objectives: first, to introduce one such scheme, developed by Arthur Dempster and Glen Shafer, to a wider audience; second, to present results that can reduce the computation-time complexity from exponential to linear, allowing this scheme to be implemented in many more systems.
These contributions demonstrate the vigor and fruitfulness of current research on belief functions, and their publication as a unit can serve to make that research even more vigorous. Fisher's fiducial methoda brilliant but unsatisfactory method for computing probabilities for statistical parameters from observations. In order to enjoy this reduction, some assumptions about the structure of the type of evidence represented and combined must be made.
During the past decade, research on belief functions has suffered from fragmentation; the researchers involved have been spread over so many different disciplines, meetings, and journals that they have often been unaware of each other's work. Dempster's generalization of Fisher's method produced non-additive probabilities, which combined by a general rule that I later called Dempster's rule of combination. The assumption made here is that each piece of the evidence either confirms or denies a single proposition rather than a disjunction.
Ces travaux ne peuvent pas tre rendus disponibles ailleurs sans la permission explicite du dtenteur du copyright.We are therefore able to disentangle social learning from learning from a private signal.Our main result is that subjects update on their private signal in an asymmetric way.It turns out that for decision makers which can be described by both theories, the two approaches coincide.Thus, we suggest an axiomatically based ambiguous beliefs update rule, which is needed for applications in many economic theory models.