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Title: Imbedded integration rules and their applications in Bayesian analysis
Author: Dellaportas, Petros
ISNI:       0000 0001 3421 7425
Awarding Body: Polytechnic South West
Current Institution: University of Plymouth
Date of Award: 1990
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This thesis deals with the development and application of numerical integration techniques for use in Bayesian Statistics. In particular, it describes how imbedded sequences of positive interpolatory integration rules (PIIR's) obtained from Gauss-Hermite product rules can extend the applicability and efficiency of currently available numerical methods. The numerical strategy suggested by Naylor and Smith (1982) is reviewed, criticised and applied to some examples with real and artificial data. The performance of this strategy is assessed from the viewpoint of 3 criteria: reliability, efficiency and accuracy. The imbedded sequences of PIIR’s are introduced as an alternative and an extension to the above strategy for two major reasons. Firstly, they provide a rich class of spatially ditributed rules which are particularly useful in high dimensions. Secondly, they provide a way of producing more efficient integration strategies by enabling approximations to be updated sequentially through the addition of new nodes at each step rather than through changing to a completely new set of nodes. Finally, the Improvement in the reliability and efficiency achieved by the adaption of an integration strategy based on PIIR's is demonstrated with various illustrative examples. Moreover, it is directly compared with the Gibbs sampling approach introduced recently by Gelfand and Smith (1988).
Supervisor: Not available Sponsor: University of Sheffield
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Numerical integration techniques