Introduction to Inverse Problems in Applied Statistics
About the Workshop
The focus of this workshop is on processes that can only be studied indirectly, such as remote sensing in environmental science or geophysics, electrical tomography in industrial process modelling or positron emission tomography in medical imaging. Each of these processes can be studied under the common framework of Inverse Problems, an exciting research frontier that combines advanced techniques from both statistical research and applied mathematics.
This half-day workshop will cover core components and fundamental concepts in a tutorial style (Session 1), and then build an understanding of state-of-the-art techniques through applications (Session 2). The workshop will draw upon almost 30 years’ experience of interdisciplinary research, using a holistic approach that addresses a broad range of mathematical, computational and applications-driven topics. In particular, linear problems in geophysics (magnetometry) and medicine (SPECT/PET), and nonlinear problems in engineering and medicine (electrical tomography) will be introduced and discussed. From a statistical point of view, these can be seen as multicollinear regression problems.
Important topics to be covered include statistical model construction, parameterization and prior specification in nonparametric statistics, posterior inference and computation with Markov chain Monte Carlo methods.
The first session is aimed at researchers across all mathematical and physical sciences looking to increase their skill and knowledge in the important, emerging area of Inverse Problems. This will provide sufficient background to allow a good appreciation of the key points in the applications session. The second session will also appeal as a standalone for those who already have a background in some area of Inverse Problems but who would like to see other applications, and learn about new approaches to modelling, statistical estimation and computation.
About the Instructor
Robert Aykroyd graduated in 1985 from the University of Newcastle-upon-Tyne and received MSc and PhD degrees in Statistics from the University of Sheffield. He has been at the University of Leeds since 1993. He has a long track record of successful innovation in the area of statistical and computational methods for inverse problems. His main interests are in the use of Bayesian modelling approaches in image analysis and other inverse problems. This has involved applications in archaeological geophysics, medical imaging (including SPECT/PET) and engineering applications of electrical tomography. He has been an investigator on several related externally funded projects, has successfully supervised research students and has over 40 publications in the area. He is currently the Editor of Journal of Applied Statistics.
9:00 Introduction and Session 1: Fundamental Concepts in Inverse Problems
11:00 Coffee Break
11:30 Session 2: Advances in the Application of Inverse Problems
13.00 End of Workshop (followed by an optional lunch with the speaker)
Participation in the workshop is free but registration on this website is required if you wish to attend. The room booking details will be sent out via email to registered participants prior to the start of the workshop.
Dr Aykroyd is a Visiting Fellow at UTS under the Key Technology Partnership scheme, joint with the University of Leeds, UK.
All email correspondance should be addressed to Lucia.Kralova@uts.edu.au.