This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 177
Type: Contributed
Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #307999
Title: Statistical Theory Using Computer-Aided Reasoning
Author(s): Leif Johnson*+
Companies: University of Minnesota
Address: 313 Ford Hall, Minneapolis, MN, 55455,
Keywords: formal proof ; theorems ; computing ; computer aided reasoning
Abstract:

Like any Mathematical theory, Statistics is constructed using by starting from a set of axioms and rules of inference. In the ideal setting, we use the axioms, rules of inference and existing theorems to prove new theorems. However, this can be difficult to execute correctly and completely by hand. In Computer Aided Reasoning (CAR), a computer program is used to verify, and sometimes deduce, the necessary steps to prove a new theorem. CAR has two main benefits, first, it gives us a greater degree of certainty that a proof is correct, and second, the computers superior book-keeping ability allows us to approach more complicated proofs. We will discuss a proof of the Markov Inequality inside a CAR system. This will include examining the necessary assumptions, and what difficulties CAR introduces.


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