Bayesian spatial data analyses and their applications /
Conventional geostatistical methodology solves the problem of predicting unknowns using Gaussian distributional and stationarity assumptions. However, sometimes these assumptions are clearly violated because of a wide range of observed locations, underlying physical reasons, etc. So, it is desirable...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
2001.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=725921711&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Conventional geostatistical methodology solves the problem of predicting unknowns using Gaussian distributional and stationarity assumptions. However, sometimes these assumptions are clearly violated because of a wide range of observed locations, underlying physical reasons, etc. So, it is desirable to extend analyses beyond usual distributional and stationarity assumptions. First of all, under the stationarity assumption, we propose Bayesian approaches to predict at unknown spatial locations based on two non-Gaussian distribution families. One is the elliptical distribution and the other is the skew Gaussian distribution. Sometimes it is natural to think of the real data as generated values from a heavy tailed distribution such as the elliptical distribution. So, a Bayesian spatial prediction model is developed on the basis of the elliptical distribution. Furthermore, a model based on skew Gaussian distribution is presented to handle skewed spatial data. It extends the results of popular Gaussian process models. Finally, piecewise Gaussian processes using a Bayesian hierarchical model are proposed, motivated by non-stationary spatial data. The study region is partitioned into several homogeneous subregions and the Gaussian process is fitted within each subregion. The final prediction is obtained using a mixture of Gaussian processes which will be smooth due to model mixing. |
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| Item Description: | Vita. "Major Subject: Statistics". |
| Physical Description: | ix, 69 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references (leaves 61-65). |