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Statistical models based on stochastic partial differential equations

Project

Project Details

Program
Statistics
Field of Study
​Statistics
Division
Computer, Electrical and Mathematical Sciences and Engineering
Faculty Lab Link
https://www.kaust.edu.sa/en/study/faculty/david-bolin

Project Description

The student will learn about modern statistical methods based on stochastic partial differential equations (SPDEs). One important advantage with formulating statistical models using SPDEs is that it facilitates non-Gaussian extensions of several popular Gaussian models. Such extensions are useful for applications where the data has features that cannot be captured by Gaussian models. The goal of the project is to implement and compare these models for applications to longitudinal medical data and spatial environmental data.

About the Researcher

David Bolin
Associate Professor, Statistics
Computer, Electrical and Mathematical Science and Engineering Division

Affiliations

Education Profile

  • Postdoctoral Fellow, UmeA¥ University, 2012-2013
  • Ph.D. Mathematical Statistics, Lund University, 2012
  • M.S. Engineering Mathematics, Lund University, 2007

Research Interests

a€‹Professor Bolina€˜s main research interests are in stochastic partial differential equations and their applications in statistics, with a focus on development of practical, computationally efficient tools for modelling non-stationary and non-Gaussian processes. He also works on uncertainty quantification and visualization for applications in spatial statistics and medical imaging.

Selected Publications

  • D. Bolin, K. Kirchner (2019), The rational SPDE approach for Gaussian random fields with general smoothness, Journal of Computational and Graphical Statistics, To appear.
  • D. Bolin, K. Kirchner, M. KovA¡cs (2018), Numerical solution of fractional elliptic stochastic PDEs with spatial white noise, IMA Journal of Numerical Analysis, dry091
  • D. Bolin and F. Lindgren (2015), Excursion and contour uncertainty regions for latent Gaussian models, Journal of the Royal Statistical Society, Series B Methodology, 77, 1, 85-106.
  • D. Bolin (2014), Spatial MatA©rn fields driven by non-Gaussian noise, Scandinavian journal of statistics, 41:3, 557-579.
  • D. Bolin and F. Lindgren (2011), Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping, Annals of Applied Statistics, 5, 1, 523-550.

Desired Project Deliverables

​​Written report and computer code that reproduces the results
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3-6 months
Internship period
100+
Research Projects
3.5/4
Cumulative GPA
310
Interns a Year