Student research opportunities

Modelling non-Gaussian spatio-temporal environmental data CSIRO PhD top-up $15000 per year available for application

Project Code: CECS_855

This project is available at the following levels:
PhD
Please note that this project is only for higher degree (postgraduate) applicants.

Keywords:

non-Gaussian processes, covariance function, computation

Supervisors:

Dr Warren Jin
Professor Marcus Hutter

Outline:

Gaussian processes are well understood and widely used by statistics, machine learning and scientific communities because of their stability and relatively computational and theoretical tractability (see e.g., Cressie and Wikle 2011, Rasmussen and Williams 2006). However, for a wide range of environmental data, such as daily precipitation, pollutant concentrations, pollen, and soil moisture, Gaussian spatio-temporal models cannot reasonably be fitted to the observations.

This project will develop non-Gaussian spatio-temporal models for data that may be zero inflated, skewed, and/or long-tailed. One direction is to transform a Gaussian process in a way that fits observations, with the potential use of some kind of link functions, like those in generalised linear regression. Care must be taken in the spatial prediction and/or temporal projection step as the covariance function in the transformed space is different, actually biased, from the one in the original space. Computation efficiency will become another issue for normally very large environmental data sets. Another direction is to assume that the spatio-temporal environmental data follow specific processes such as t-process or Gamma processes. Challenges here will be around theoretical development of the models, appropriate covariance functions, and efficient computation (such as reduced rank approximation, tapering, Gaussian predictive processes).

Goals of this project

The project will develop sophisticated models based on non-Gaussian processes or asymptotic Gaussian processes, and implement associated software. These developed techniques are applicable to various environmental problems such as daily precipitation projection, extreme weather modelling, remote sensed data, climate change attribution, and so on. It will also impact these important areas by combining sophisticated statistical modelling techniques with modern computation techniques.

Requirements/Prerequisites

Applicants are expected to have a major in statistics/mathematics, or computer science.

Strong interest in environmental problems

Preferably with strong background in statistical machine learning or statistical computation.

Preferably with excellent programming skills (R, MatLab or C/C++)

Student Gain

A student working in this project can expect

to learn state-of-art of statistical modelling and machine learning techniques

to be involved in developing cutting-edge techniques to handle real-world environmental challenges with great impact;

Supplementary PhD scholarship available from CSIRO $15000 per year for three years, subject to a separate application to CSIRO

Background Literature

Gaussian Processes for Machine Learning.
Carl Edward Rasmussen and Christopher K. I. Williams
MIT Press, 2006. ISBN-10 0-262-18253-X.

Porcu et al. (eds.), Advances and Challenges in Space-time Modelling of Natural Events. Springer, 2012.

Cressie, N., T. Shi, and E. L. Kang (2010), Fixed Rank Filtering for Spatio-Temporal Data, Journal of Computational and Graphical Statistics, 19(3), 724-745, DOI 10.1198/jcgs.2010.09051;

Reinhard Furrer and Stephan R. Sain,
Spatial model fitting for large datasets with applications to climate and microarray problems.
Statistics and Computing. Volume 19, Number 2 (2009), 113-128, DOI: 10.1007/s11222-008-9075-x