Reliable calculation in probabilistic logic: Accounting for small sample size and model uncertainty
- Applied Biomathematics, Setauket, NY (United States)
A variety of practical computational problems arise in risk and safety assessments, forensic statistics and decision analyses in which the probability of some event or proposition E is to be estimated from the probabilities of a finite list of related subevents or propositions F,G,H,.... In practice, the analyst`s knowledge may be incomplete in two ways. First, the probabilities of the subevents may be imprecisely known from statistical estimations, perhaps based on very small sample sizes. Second, relationships among the subevents may be known imprecisely. For instance, there may be only limited information about their stochastic dependencies. Representing probability estimates as interval ranges on has been suggested as a way to address the first source of imprecision. A suite of AND, OR and NOT operators defined with reference to the classical Frochet inequalities permit these probability intervals to be used in calculations that address the second source of imprecision, in many cases, in a best possible way. Using statistical confidence intervals as inputs unravels the closure properties of this approach however, requiring that probability estimates be characterized by a nested stack of intervals for all possible levels of statistical confidence, from a point estimate (0% confidence) to the entire unit interval (100% confidence). The corresponding logical operations implied by convolutive application of the logical operators for every possible pair of confidence intervals reduces by symmetry to a manageably simple level-wise iteration. The resulting calculus can be implemented in software that allows users to compute comprehensive and often level-wise best possible bounds on probabilities for logical functions of events.
- OSTI ID:
- 466442
- Report Number(s):
- CONF-9610138-; CNN: Grant GM49521; TRN: 97:001309-0021
- Resource Relation:
- Conference: International multi-disciplinary conference on intelligent systems: a semiotic perspective, Gaithersburg, MD (United States), 21-23 Oct 1996; Other Information: PBD: 1996; Related Information: Is Part Of Intelligent systems: A semiotic perspective. Volume I: Theoretical semiotics; Albus, J.; Meystel, A.; Quintero, R.; PB: 303 p.
- Country of Publication:
- United States
- Language:
- English
Similar Records
Comparing probabilistic and descriptive analyses of time–dose–toxicity relationship for determining no-observed-adverse-effect level in drug development
Classical foundations of quantum logic