Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction
A class of models for non-Gaussian spatial random fields is explored for spatial field reconstruction in environmental and sensor network monitoring. The family of models explored utilises a class of transformation functions known as Tukey g-and-h transformations to create a family of warped spatial...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/10/1323 |
| _version_ | 1797514689076264960 |
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| author | Gareth W. Peters Ido Nevat Sai Ganesh Nagarajan Tomoko Matsui |
| author_facet | Gareth W. Peters Ido Nevat Sai Ganesh Nagarajan Tomoko Matsui |
| author_sort | Gareth W. Peters |
| collection | DOAJ |
| description | A class of models for non-Gaussian spatial random fields is explored for spatial field reconstruction in environmental and sensor network monitoring. The family of models explored utilises a class of transformation functions known as Tukey g-and-h transformations to create a family of warped spatial Gaussian process models which can support various desirable features such as flexible marginal distributions, which can be skewed, leptokurtic and/or heavy-tailed. The resulting model is widely applicable in a range of spatial field reconstruction applications. To utilise the model in applications in practice, it is important to carefully characterise the statistical properties of the Tukey g-and-h random fields. In this work, we study both the properties of the resulting warped Gaussian processes as well as using the characterising statistical properties of the warped processes to obtain flexible spatial field reconstructions. In this regard we derive five different estimators for various important quantities often considered in spatial field reconstruction problems. These include the multi-point Minimum Mean Squared Error (MMSE) estimators, the multi-point Maximum A-Posteriori (MAP) estimators, an efficient class of multi-point linear estimators based on the Spatial-Best Linear Unbiased (S-BLUE) estimators, and two multi-point threshold exceedance based estimators, namely the Spatial Regional and Level Exceedance estimators. Simulation results and real data examples show the benefits of using the Tukey g-and-h transformation as opposed to standard Gaussian spatial random fields in a real data application for environmental monitoring. |
| first_indexed | 2024-03-10T06:35:09Z |
| format | Article |
| id | doaj.art-e4bd8fb3defc4ece9a4cca49e58525a7 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T06:35:09Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-e4bd8fb3defc4ece9a4cca49e58525a72023-11-22T18:11:16ZengMDPI AGEntropy1099-43002021-10-012310132310.3390/e23101323Spatial Warped Gaussian Processes: Estimation and Efficient Field ReconstructionGareth W. Peters0Ido Nevat1Sai Ganesh Nagarajan2Tomoko Matsui3Department of Statistics and Applied Probability, University of California Santa Barbara, Santa Barbara, CA 93106, USATUMCREATE, 1 Create Way, #10-02 CREATE Tower, Singapore 138602, SingaporeEngineering Systems and Design Pillar, Singapore University of Technology and Design (SUTD), 8 Somapah Road, Singapore 487372, SingaporeDepartment of Statistical Modeling, The Institute of Statistical Mathematics (ISM), 10-3 Midoricho, Tachikawa, Tokyo 190-0014, JapanA class of models for non-Gaussian spatial random fields is explored for spatial field reconstruction in environmental and sensor network monitoring. The family of models explored utilises a class of transformation functions known as Tukey g-and-h transformations to create a family of warped spatial Gaussian process models which can support various desirable features such as flexible marginal distributions, which can be skewed, leptokurtic and/or heavy-tailed. The resulting model is widely applicable in a range of spatial field reconstruction applications. To utilise the model in applications in practice, it is important to carefully characterise the statistical properties of the Tukey g-and-h random fields. In this work, we study both the properties of the resulting warped Gaussian processes as well as using the characterising statistical properties of the warped processes to obtain flexible spatial field reconstructions. In this regard we derive five different estimators for various important quantities often considered in spatial field reconstruction problems. These include the multi-point Minimum Mean Squared Error (MMSE) estimators, the multi-point Maximum A-Posteriori (MAP) estimators, an efficient class of multi-point linear estimators based on the Spatial-Best Linear Unbiased (S-BLUE) estimators, and two multi-point threshold exceedance based estimators, namely the Spatial Regional and Level Exceedance estimators. Simulation results and real data examples show the benefits of using the Tukey g-and-h transformation as opposed to standard Gaussian spatial random fields in a real data application for environmental monitoring.https://www.mdpi.com/1099-4300/23/10/1323random fieldswarped Gaussian processspatial field reconstruction |
| spellingShingle | Gareth W. Peters Ido Nevat Sai Ganesh Nagarajan Tomoko Matsui Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction Entropy random fields warped Gaussian process spatial field reconstruction |
| title | Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction |
| title_full | Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction |
| title_fullStr | Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction |
| title_full_unstemmed | Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction |
| title_short | Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction |
| title_sort | spatial warped gaussian processes estimation and efficient field reconstruction |
| topic | random fields warped Gaussian process spatial field reconstruction |
| url | https://www.mdpi.com/1099-4300/23/10/1323 |
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