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MIT16_410F10_lec19b

# MIT16_410F10_lec19b - Probabilistic Model-based Diagnosis...

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3/6/00 1 Probabilistic Model-based Diagnosis 10/28/07 copyright Brian Williams, 2005-09 1 Brian C. Williams 16.410/16.413 November 17 th , 2010 Brian C. Williams, copyright 2000-09 Notation S t+1 set of hidden variables in the t+1 time slice s t+1 set of values for those hidden variables at t+1 o t+1 set of observations at time t+1 o 1:t set of observations from all times from 1 to t α normalization constant 10/28/07 copyright Brian Williams, 2005-09 2 Image credit: NASA.

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3/6/00 2 Multiple Faults Occur three shorts, tank-line and pressure jacket burst, panel flies off. Lecture 12: Framed as CSP. How do we compare the space of alternative diagnoses? How do we prefer diagnoses that explain failure? 10/28/07 copyright Brian Williams, 2005-09 3 APOLLO 13 Image source: NASA. Due to the unknown mode, there tends to be an exponential number of diagnoses. U Candidates with UNKNOWN failure modes Good G Candidates with KNOWN failure modes Good F1 Fn G U U 10/26/10 4 1. Introduce fault models. More constraining, hence more easy to rule out. Increases size of candidate space. 2. Enumerate most likely diagnoses X i based on probability. Prefix (k) ( Sort {X i } by decreasing P(X i | O) ) Most of the probability mass is covered by a few diagnoses.
3/6/00 3 Model-based Diagnosis Input: Finite Domain Variables <X,Y> X mode variables Y model variables O observable variables O Y. Φ(X, Y) model constraints o observations o i:n D O P(X i ) a prior probability of modes Output: {x D X | y D Y s.t. x o Φ(x,y) is consistent} Consistency-based

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• Fall '10
• Prof.BrianWilliams
• Probability theory, Bayesian probability, Prior probability, Brian C. Williams, copyright Brian Williams

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