**HEAD Division Meeting 1999, April 1999**

*Session 33. Other*

Poster, Wednesday, April 14, 1999, 8:30am Wed. - 2:00pm Thurs., Gold Room
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## [33.06] Analysis of Energy Spectrum with Low Photon Counts via Bayesian Posterior Simulation

*David A. van Dyk, Rostislav Protassov (Harvard University), Vinay L. Kashyap, Aneta Siemiginowska (Harvard-Smithsonian Center for Astrophysics), Alanna Connors (Wellesley College)*

Recently Bayesian methods have grown rapidly in popularity
in many scientific disciplines as several computationally
intensive statistical algorithms have become feasible with
modern computer power. In this paper, we demonstrate how we
have employed these state-of-the-art techniques (e.g., Gibbs
sampler and Metropolis-Hastings) to fit today's
high-quality, high resolution astrophysical spectral data.
These algorithms are very flexible and can be used to fit
models that account for the highly hierarchical structure in
the collection of high-quality spectra and thus can keep
pace with the accelerating progress of new telescope
designs. 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. These methods will be
useful not only for the soon-to-be-launched Chandra X-ray
observatory but also such new generation telescopes as XMM,
Constellation X, and GLAST.

We also explicitly incorporate the instrument response (e.g.
via a response matrix and effective area vector), plus
background contamination of the data. In particular, we
appropriately model the background as the realization of a
second Poisson process, thereby eliminating the need to
directly subtract off the background counts and the rather
embarrassing problem of negative photon counts. The source
energy spectrum is modeled as a mixture of a Generalized
Linear Model which accounts for the continuum plus
absorption and several (Gaussian) line profiles. Generalized
Linear Models are the standard method for incorporating
covariate information (as in regression) into non-Gaussian
models and are thus an obvious but innovative choice in this
setting. Using several examples, we illustrate how Bayesian
posterior sampling can be used to compute point (i.e.,
``best'') estimates of the various model parameters as well
as compute error bars on these estimates and construct
statistical tests.

If the author provided an email address or URL for general inquiries,
it is as follows:

vandyk@stat.harvard.edu

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