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Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes

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  • Fangpo Wang
  • Alan E. Gelfand

Abstract

Directional data naturally arise in many scientific fields, such as oceanography (wave direction), meteorology (wind direction), and biology (animal movement direction). Our contribution is to develop a fully model-based approach to capture structured spatial dependence for modeling directional data at different spatial locations. We build a projected Gaussian spatial process, induced from an inline bivariate Gaussian spatial process. We discuss the properties of the projected Gaussian process and show how to fit this process as a model for data, using suitable latent variables, with Markov chain Monte Carlo methods. We also show how to implement spatial interpolation and conduct model comparison in this setting. Simulated examples are provided as proof of concept. A data application arises for modeling wave direction data in the Adriatic sea, off the coast of Italy. In fact, this directional data is available across time, requiring a spatio-temporal model for its analysis. We discuss and illustrate this extension.

Suggested Citation

  • Fangpo Wang & Alan E. Gelfand, 2014. "Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1565-1580, December.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:508:p:1565-1580
    DOI: 10.1080/01621459.2014.934454
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    References listed on IDEAS

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    1. Kato, Shogo & Jones, M. C., 2010. "A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 249-262.
    2. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    3. Shogo Kato, 2010. "A Markov process for circular data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 655-672, November.
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    Cited by:

    1. Fangpo Wang & Anirban Bhattacharya & Alan E. Gelfand, 2018. "Process modeling for slope and aspect with application to elevation data maps," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 749-772, December.
    2. Mastrantonio, Gianluca, 2018. "The joint projected normal and skew-normal: A distribution for poly-cylindrical data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 14-26.
    3. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    4. Jan Beran & Sucharita Ghosh, 2020. "Estimating the Mean Direction of Strongly Dependent Circular Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 210-228, March.
    5. Xu Gao & Babak Shahbaba & Hernando Ombao, 2018. "Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 549-579, October.
    6. Saralees Nadarajah & Yuanyuan Zhang, 2017. "Wrapped: An R package for circular data," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-26, December.
    7. Jan Beran & Britta Steffens & Sucharita Ghosh, 2022. "On nonparametric regression for bivariate circular long-memory time series," Statistical Papers, Springer, vol. 63(1), pages 29-52, February.

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