Mathematical Sciences: Coherent Studies in Conditional      Probability
{'Code': '03040107', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Peter Arzberger', 'PO_EMAI': None, 'PO_PHON': None}
The project will study the coherence concepts for a given                  assessment of likelihood.  The whole field of Bayesian analysis                 is based on the subjective assignments of probabilities to the                  observed events.  Such assignments are only locally coherent.  On               the other hand the measure theoretic model for probabilities                    requires countable additivity of the probabilities, a condition                 that is hard to accept on philosophical grounds.  A theory will                 be developed to address questions of both coherence and                         mathematical properties such as countable additivity.  The theory               will be developed based on the concepts of upper and lower                      exchange rates.  The research will have applications to non-                    Boolean event structures of quantum mechanics necessary to give                 notions of quantum probability.
{'FirstName': 'Thomas', 'LastName': 'Armstrong', 'PI_MID_INIT': 'E', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Thomas E Armstrong', 'EmailAddress': None, 'NSF_ID': '000384469', 'StartDate': '07/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1263', 'Text': 'PROBABILITY'}
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