This chapter proposes a notion of independence in the conditional possibility theory, which encompasses the critical situations presented by other independence definitions. The conditional possibility is directly defined as a function on a set (with a suitable algebraic structure) of conditional events, in such a way that π (. E|H) makes sense for any pair of events E and H, with H ≠ Ø, and it must satisfy proper axioms. A characterization theorem of conditional possibility in terms of a class of unconditional possibility measures allows introducing a new notion of independence, which is a formal counterpart of stochastic independence in the framework of coherent conditional probability. The proposed independence notion can be generalized to conditional independence among random variables
Independence in conditional possibility theory.
COLETTI, Giulianella;
2006
Abstract
This chapter proposes a notion of independence in the conditional possibility theory, which encompasses the critical situations presented by other independence definitions. The conditional possibility is directly defined as a function on a set (with a suitable algebraic structure) of conditional events, in such a way that π (. E|H) makes sense for any pair of events E and H, with H ≠ Ø, and it must satisfy proper axioms. A characterization theorem of conditional possibility in terms of a class of unconditional possibility measures allows introducing a new notion of independence, which is a formal counterpart of stochastic independence in the framework of coherent conditional probability. The proposed independence notion can be generalized to conditional independence among random variablesI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.