No abstract

Model comparison for the purposes of selection, averaging, and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a particular class. Substantial progress has been made in recent years, but difficulties remain in the implementation of existing schemes. This article presents adaptive sequential Monte Carlo (SMC) sampling strategies to characterize the posterior distribution of a collection of models, as well as the parameters of those models. Both a simple product estimator and a combination of SMC and a path sampling estimator are considered and existing theoretical results are extended to include the path sampling variant. A novel approach to the automatic specification of distributions within SMC algorithms is presented and shown to outperform the state of the art in this area. The performance of the proposed strategies is demonstrated via an extensive empirical study. Comparisons with stateof-the-art algorithms show that the proposed algorithms are always competitive, and often substantially superior to alternative techniques, at equal computational cost and considerably less application-specific implementation effort. Supplementary materials for this article are available online.

A kinetic modeling approach for the quantification of in vivo tracer studies with dynamic positron emission tomography (PET) is presented. The approach is based on a general compartmental description of the tracer's fate in vivo and determines a parsimonious model consistent with the measured data. The technique involves the determination of a sparse selection of kinetic basis functions from an overcomplete dictionary using the method of basis pursuit denoising. This enables the characterization of the systems impulse response function from which values of the systems macro parameters can be estimated. These parameter estimates can be obtained from a region of interest analysis or as parametric images from a voxel-based analysis. In addition, model order estimates are returned that correspond to the number of compartments in the estimated compartmental model. Validation studies evaluate the methods performance against two preexisting data led techniques, namely, graphical analysis and spectral analysis. Application of this technique to measured PET data is demonstrated using [11C]diprenorphine (opiate receptor) and [11C]WAY-100635 (5-HT1A receptor). Although the method is presented in the context of PET neuroreceptor binding studies, it has general applicability to the quantification of PET/SPECT radiotracer studies in neurology, oncology, and cardiology.