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Paper No. 11-26

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Y Zhou, JAD Aston and A Johansen

Bayesian Model Comparison for Compartmental Models with Applications in Positron Emisson Tomography

Abstract: We develop strategies for Bayesian modelling as well as model comparison, averaging and selection for compartmental models with particular emphasis on those which occur in the analysis of Positron Emission Tomography (PET) data. Both modelling and computational issues are considered. It is shown that an additive normal error structure does not describe measured PET data well and that within a simple Bayesian framework simultaneous parameter estimation and model comparison can be performed with a more general noise model. The proposed methodology is compared to standard techniques using both simulated and real data. In addition to good estimation performance, the proposed technique provides, automatically, a characterisation of the uncertainty in the resulting estimates which can be considerable in applications such as PET.

Keywords: Model Selection; Model Averaging; Compartmental Models