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R. S. Protassov, D. A. van Dyk, D. Esch (Dept. of Statistics, Harvard University), A. Conners (Wellesley College), V. L. Kashyap, A. Siemiginowska (Harvard-Smithsonian Center for Astrophysics)
In this talk, we briefly illustrate how we have employed state-of-the-art Bayesian computational techniques (e.g., the Gibbs sampler and Metropolis-Hastings) and inferencial methods (e.g., posterior-predictive p-values) to handle numerous data analytic difficulties with the high-resolution low-count data of the Chandra X-ray Observatory and similar issues that will arise with other new generation telescopes such as XMM, Constellation-X, and GLAST. For such important problems as testing for a spectral line or a spatial feature, we consider Bayesian solutions which expose unexpected failures of standard methods. We explore Markov random fields with added structure to model spatial images and consider new models which allow the spectrum to change smoothly across the image. Finally we exploit highly computationally intensive methods to adjust for the pile-up of photons, accounting for event grade information. In particular, we formulate models that account for the complex structure in the collection of high-quality spectral and spatial data. We explicitly model photon arrivals as a Poisson process and, thus, have no difficulty with high resolution low count X-ray and gamma-ray data. Instrument response (e.g., quantified via a response matrix , effective area vector, and point spread function) and background contamination of the data are explicitly incorportated into the analysis, thereby eliminating the need to directly subtract off the background counts and the rather embarrassing problem of negative photon counts.
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The author(s) of this abstract have provided an email address for comments about the abstract: protass@stat.harvard.edu