Over the past 10 years Bayesian methods have rapidly grown more popular in many scientific disciplines as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper we begin with a general description of the Bayesian paradigm for statistical inference and the various state-of-the-art model-fitting techniques that we employ (e.g., the Gibbs sampler and the Metropolis-Hastings algorithm). These algorithms are very flexible and can be used to Dt models that account for the highly hierarchical structure inherent in the collection of high-quality spectra and thus can keep pace with the accelerating progress of new space telescope designs. The methods we develop, which will soon be available in the Chandra Interactive Analysis of Observations (CIAO) software, explicitly model photon arrivals as a Poisson process and thus have no difficulty with high-resolution low-count X-ray and gamma -ray data. We expect 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 Constellation X, GLAST, etc. In the context of two examples (quasar S5 0014+813 and hybrid-chromosphere supergiant star alpha TrA), we illustrate a new highly structured model and how Bayesian posterior sampling can be used to compute estimates, error bars, and credible intervals for the various model parameters. Application of our method to the high-energy tail of the ASCA spectrum of alpha TrA confirms that even at a quiescent state, the coronal plasma on this hybrid-chromosphere star is indeed at high temperatures (>10 MK) that normally characterize flaring plasma on the Sun. We are also able to constrain the coronal metallicity and find that although it is subject to large uncertainties, it is consistent with the photospheric measurements.
The solar neutrino data are analysed in a frequentist framework, using the Crow-Gardner and Feldman-Cousins prescriptions for the construction of confidence regions. Including in the fit only the total rates measured by the various experiments, both methods give results similar to the commonly used Delta chi (2)-cut approximation. When fitting the full data set, the Delta chi (2)-cut still gives a good approximation of the Feldman-Cousins regions. However, a careful statistical analysis significantly reduces the goodness-of-fit of the SMA and LOW solutions.
We study the Q(2) dependence of large x F-2 nucleon structure function data, with the aim of providing a perturbative QCD based, quantitative analysis of parton-hadron duality. As opposed to previous analyses at fixed x, we use a framework in fixed W-2. We uncover a breakdown of the twist-4 approximation with a renormalon type improvement at O(1/Q(4)) which affects the initial evolution of parton distributions.
Abstract We apply the method of principal component analysis to a sample of simple stellar populations to select some age-sensitive spectral indices. Besides the well-known age-sensitive index, Hβ, we find that some other spectral indices have great potential to determine the age of stellar populations, such as G4300, Fe4383, C24668, and Mgb. In addition, we find that the sensitivity to age of these spectral indices depends on the metallicity of the simple stellar population (SSP): Hβ and G4300 are more suited to determine the age of the low-metallicity stellar population, C24668 and Mgb are more suited to the high-metallicity stellar population. The results suggest that the principal component analysis method provides a more objective and informative alternative to diagnostics by individual spectral lines.