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Bayesian multivariate interpolation with missing data and its applications Sun, Weimin
Abstract
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.
Item Metadata
Title |
Bayesian multivariate interpolation with missing data and its applications
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1994
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Description |
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.
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Extent |
2465492 bytes
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Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-06-11
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0088917
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1995-05
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.