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Bayesian multivariate interpolation with missing data and its applications

University of British Columbia

This thesis develops Bayesian multivariate interpolation theories when there are: (i) data missing-by-design; (ii) randomly missing data; (iii) monotone missing data patterns. Case (i) is fully discussed both theoretically and empirically. A predictive distribution yields a Bayesian interpolator with associated standard deviation, a simultaneous interpolation region, and a hyperparameter estimation algorithm. These results are described in detail. The method is applied to interpolating data from Southern Ontario Pollution. An optimal redesign of a current network is proposed. A cross-validation study is conducted to judge the performance of our method. The method is compared with a Co-kriging approach to which the method is meant to be an alternate. Case (ii) is briefly discussed. An approximation of a matrix T-distribution by a normal distribution is explored for obtaining an approximate predictive distribution. Based on the approximate distribution, an approximate Bayesian interpolator and an approach for estimating hyperparameters by the EM algorithm are described. Case (iii) is only touched on. Only an iterative predictive distribution is derived. Further study is needed for finding ways of estimating hyperparameters.

Thesis/Dissertation

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2009-06-11

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http://hdl.handle.net/2429/8976

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University of British Columbia

UBCV

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