Emission tomography and Bayesian inverse problems

Host Institution:

The University of Sydney

Title of Seminar:

Emission tomography and Bayesian inverse problems

Speaker's Name:

Professor Peter J. Green

Speaker's Institution:

University of Technology, Sydney, and University of Bristol

Time and Date:

Friday 26 October, 2.00 PM EDT

Seminar Abstract:

 

Inverse problems are almost ubiquitous in applied science and technology, so have long been a focus for intensive study, aimed at both methodological development and theoretical analysis. Formulating inverse problems as questions of Bayesian inference has great appeal in terms of coherence, interpretability and integration of uncertainty: the Bayesian formulation comes close to the way that most scientists intuitively regard the inferential task, and in principle allows the free use of subject knowledge in probabilistic model building. However, it is important to understand the relationship between the chosen Bayesian model and the resulting solution.

We discuss the Bayesian approach to reconstruction in single-photon emission computed tomography, giving several empirical illustrations. We also present theoretical results from joint work with Natalia Bochkina (Edinburgh) about consistency of the posterior distribution of the reconstruction, and a version of the Bernstein--von Mises theorem that quantifies the efficiency of Bayesian inference for such ill-posed generalised linear inverse problems with constraints.

About Peter Green:
I am a statistical scientist, principally interested in Bayesian inference in complex stochastic systems, Markov chain Monte Carlo methodology, forensic genetics, Bayesian nonparametrics, and graphical models.

Before moving to Bristol to a Chair of Statistics in 1989, I had been lecturing at the Universities of Bath (1974-1978) and Durham (1978-1989). I have now retired from my full-time role at Bristol, but hold an Emeritus Professorship and Professorial Research Fellowship there, as well as a Distinguished Professorship at UTS. I have collaborations with researchers in the USA, in Italy and in Denmark, and, formerly, in Norway, Canada and Singapore.

I have been awarded a Royal Society Wolfson Research Merit Award (2006-11), Fellowship of the Royal Society (2003), Chartered Statistician (2001), Guy Medal in Silver, Royal Statistical Society (1999), Fellowship of the Institute of Mathematical Statistics (1991) and Guy Medal in Bronze, Royal Statistical Society (1987).

My main web page is at http://www.stats.bris.ac.uk/~peter/

 

Seminar Convenor:

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AGR IT support: