A Bayesian decision approach to model monitoring and cusums

A Bayesian decision approach to model monitoring and cusums

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Article ID: iaor19942530
Country: United Kingdom
Volume: 13
Issue: 1
Start Page Number: 29
End Page Number: 36
Publication Date: Jan 1994
Journal: International Journal of Forecasting
Authors: ,
Keywords: Bayesian forecasting
Abstract:

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.

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