Multi-Process Models

  • Mike West
  • Jeff Harrison
Part of the Springer Series in Statistics book series (SSS)


Discussion of interventionist ideas and monitoring techniques is an implicit acknowledgement of the principle that, although an assumed DLM form may be accepted as appropriate for a series, the global behaviour of the series may only be adequately mirrored by allowing for changes from time to time in model parameters and defining structural features. Intervention allows for parametric changes, and goes further by permitting structural changes to be made to the defining quadruple {F, G, V, W} t . In using automatic monitoring techniques, as in Section 11.4 of Chapter 11, the construction of specific alternative models rather explicity recognises the global inadequacy of any single DLM, introducing possible explanations of the inadequacies. The simple use of such alternatives to provide comparison with a standard, chosen model is taken much further in this chapter. We formalise the notion of explicit alternatives by considering classes of DLMs, the combination of models across a class providing an overall super-model for the series. This idea was originally developed in Harrison and Stevens (1971), and taken further in Harrison and Stevens (1976a). We refer to such combinations of basic DLMs as multi-process models; any single DLM defines a process model, the combination of several defines a multi-process model. Loosely speaking, the combining is effected using discrete probability mixtures of DLMs, and so multi-process models may be alternatively referred to simply as mixture models. Following Harrison and Stevens (1976a), we distinguish two classes of multi-process models, Class I and Class II, that are fundamentally different in structure and serve rather different purposes in practice. The two classes are formally defined and developed throughout the chapter after first providing a general introduction.


Posterior Probability Posterior Distribution Discount Factor Growth Change Predictive Density 
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Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • Mike West
    • 1
  • Jeff Harrison
    • 2
  1. 1.Institute of Statistics and Decision SciencesDuke UniversityDurhamUSA
  2. 2.Department of StatisticsUniversity of WarwickCoventryUK

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