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Activity Number:
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541
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Type:
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Contributed
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Date/Time:
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Thursday, August 10, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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Biopharmaceutical Section
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| Abstract - #307156 |
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Title:
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Distributions of Patterns in Markov Chains with Stopping Rules
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Author(s):
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Francis Hsuan*+ and Milton Parnes and Thomas E. Bradstreet
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Companies:
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Temple University and Temple University and Merck Research Laboratories
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Address:
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, Philadelphia, PA, 19122,
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Keywords:
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Mathematica ; embedded Markov chain ; potential function
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Abstract:
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Markov-chain potential theory provides a simple and unified way to find the multivariate distributions of patterns in repeated binary data with a stopping rule. One example is the T-maze swim test in behavioral teratology experiments. Here, each rat swims up the entry channel (the base of the T) and escapes successfully only if it turns in the direction towards an a-priori chosen end of the crossbar. Each rat in the experiment is tested repeatedly until three consecutive successes are observed. The experiment results in repeated binary data, which ends in three consecutive 1's. One question is to find the joint multivariate distribution of sufficient statistics N00 (the number of two consecutive 0's in a string), N01, N10 and N11. We use potential theory to derive explicitly the joint probability generating function of minimal sufficient statistics.
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