Spatio-Temporal Data Analysis by Transformed Gaussian Processes

  • Yuan Yan

Student thesis: Doctoral Thesis

Abstract

In the analysis of spatio-temporal data, statistical inference based on the Gaussian assumption is ubiquitous due to its many attractive properties. However, data collected from different fields of science rarely meet the assumption of Gaussianity. One option is to apply a monotonic transformation to the data such that the transformed data have a distribution that is close to Gaussian. In this thesis, we focus on a flexible two-parameter family of transformations, the Tukey g-and-h (TGH) transformation. This family has the desirable properties that the two parameters g ∈ R and h ≥ 0 involved control skewness and tail-heaviness of the distribution, respectively. Applying the TGH transformation to a standard normal distribution results in the univariate TGH distribution. Extensions to the multivariate case and to a spatial process were developed recently. In this thesis, motivated by the need to exploit wind as renewable energy, we tackle the challenges of modeling big spatio-temporal data that are non-Gaussian by applying the TGH transformation to different types of Gaussian processes: spatial (random field), temporal (time series), spatio-temporal, and their multivariate extensions. We explore various aspects of spatio-temporal data modeling techniques using transformed Gaussian processes with the TGH transformation. First, we use the TGH transformation to generate non-Gaussian spatial data with the Matérn covariance function, and study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters in the Matérn covariance via a sophisticatedly designed simulation study. Second, we build two autoregressive time series models using the TGH transformation. One model is applied to a dataset of observational wind speeds and shows advantaged in accurate forecasting; the other model is used to fit wind speed data from a climate model on gridded locations covering Saudi Arabia and to Gaussianize the data for each location. Third, we develop a parsimonious spatio-temporal model for time series data on a spatial grid and utilize the aforementioned Gaussianized climate model wind speed data to fit the latent Gaussian spatio-temporal process. Finally, we discuss issues under a unified framework of modeling multivariate trans-Gaussian processes and adopt one of the TGH autoregressive models to build a stochastic generator for global wind speed.
Date of AwardDec 6 2018
Original languageEnglish (US)
Awarding Institution
  • Computer, Electrical and Mathematical Science and Engineering
SupervisorMarc Genton (Supervisor)

Keywords

  • non-gaussian
  • spatiotemporal model
  • data transformation
  • wind data

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