Analysis of energy spectra with low photon counts via Bayesian posterior simulation

Over the past 10 years Bayesian methods have rapidly grown more popular in many scientific disciplines as several computationally intensive statistica l algorithms have become feasible with increased computer power. In this pa per we begin with a general description of the Bayesian paradigm for statis tical inference and the various state-of-the-art model-fitting techniques t hat we employ (e.g., the Gibbs sampler and the Metropolis-Hastings algorith m). These algorithms are very flexible and can be used to Dt models that ac count for the highly hierarchical structure inherent in the collection of h igh-quality spectra and thus can keep pace with the accelerating progress o f new space telescope designs. The methods we develop, which will soon be a vailable in the Chandra Interactive Analysis of Observations (CIAO) softwar e, explicitly model photon arrivals as a Poisson process and thus have no d ifficulty with high-resolution low-count X-ray and gamma -ray data. We expe ct these methods to be useful not only for the recently launched Chandra X- Ray Observatory and XMM but also for new generation telescopes such as Cons tellation X, GLAST, etc. In the context of two examples (quasar S5 0014+813 and hybrid-chromosphere supergiant star alpha TrA), we illustrate a new hi ghly structured model and how Bayesian posterior sampling can be used to co mpute estimates, error bars, and credible intervals for the various model p arameters. Application of our method to the high-energy tail of the ASCA sp ectrum of alpha TrA confirms that even at a quiescent state, the coronal pl asma on this hybrid-chromosphere star is indeed at high temperatures (>10 M K) that normally characterize flaring plasma on the Sun. We are also able t o constrain the coronal metallicity and find that although it is subject to large uncertainties, it is consistent with the photospheric measurements.