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A bayesian decision approach to model monitoring and cusums
Author(s) -
Harrison P. J.,
Veerapen P. P.
Publication year - 1994
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.3980130105
Subject(s) - cusum , bayesian probability , computer science , sequence (biology) , algorithm , bayesian inference , mathematics , statistics , data mining , artificial intelligence , biology , genetics
Cumulative Sum techniques are widely used in quality control and model monitoring. A single‐sided cusum may be regarded essentially as a sequence of sequential tests which, in many cases, such as those for the Exponential Family, is equivalent to a Sequence of Sequential Probability Ratio Tests. The relationship between cusums and Bayesian decisions is difficult to establish using conventional methods. An alternative approach is proposed which not only reveals a relation but also offers a very simple formulation of the decision process involved in model monitoring. This is first illustrated for a Normal mean and then extended to other important practical cases including Dynamic Models. For V‐mask cusum graphs a particular feature is the interpretation of the distance of the V vertex from the latest plotted point in terms of the prior precision as measured in ‘equivalent’ observations.