Computation with Imprecise Probabilities--The Problem of Vera's Age
In large measure, real-world probabilities are imprecise. For this
reason, computation with imprecise probabilities is not an academic
exercise--it is a bridge to reality.
Peter Walley's 1991 seminal work "Statistical Reasoning with
Imprecise Probabilities" sparked a rapid growth of interest in
imprecise probabilities. In a 2002 special issue on imprecise
probabilities of the Journal of Statistical Planning and Inference
(JSPI), edited by Peter Walley and Jean-Marc Bernard, a number of
approaches are described. My paper in this issue, "Toward a
Perception-based Theory of Probabilistic Reasoning with Imprecise
Probabilities," breaks away from the mainstream. In the
perception-based approach, probabilities, events, utilities, relations
and constraints are assumed to be described in a natural language.
Can the mainstream approaches deal with problems in which
probabilities and everything else are described in a natural language?
Here are two relatively simple test problems which fall into this category.
1. /X/ is a real-valued random variable. My perceptions are: (a)
usually /X/ is much larger than approximately /a/; (b) usually
/X/ is much smaller than approximately /b/. What is the expected
value of /X/?
2. /X/ is Vera's age. What I know about /X/ is: (a) Vera has a son
in mid-twenties; (b) Vera has a daughter in mid-thirties; and (c)
(world knowledge) mother's age at birth of a child is usually
between approximately twenty and approximately fourty. Given this
information, how would you estimate Vera's age?
Regards to all
Lotfi
--
Lotfi A. Zadeh
Professor in the Graduate School
Director, Berkeley Initiative in Soft Computing (BISC)
Tel.(office): (510) 642-4959
Fax (office): (510) 642-1712
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