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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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  3:15 p.m., Wednesday, November 14, 2007\\
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  Building 380, Room 380-C\\
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  \textsl{Terry Fine} \\
  Cornell University
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  \subsection*{Limitations of Standard Probability Models and Some Alternatives}
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\noindent

I provide a framework for criticizing the universality of standard numerical probability in terms of considerations of expressiveness and precision/accuracy. Examples provided are: the failure of the expression of the familiar formula for the probability of a non-disjoint union of sets in quantum mechanics; long-run frequencies are typically somewhat unstable and for them we consider comparative probability models; existence of limiting relative frequencies and a noncommittal law of large numbers; partial orders for induction/inference; subjective probability. 


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