Statistics – Computation
Scientific paper
Aug 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004head....8.1633p&link_type=abstract
American Astronomical Society, HEAD meeting #8, #16.33; Bulletin of the American Astronomical Society, Vol. 36, p.934
Statistics
Computation
Scientific paper
Spectral emission lines are local features that represent extra emissions of photons in a narrow band of energy. Emission lines are important in the investigation of the chemical composition of a source, and determining the precise location of the emission lines aids in understanding the relative velocity of a source. It is often appropriate to model the emission lines with a delta function in a statistical model. Here, one of our main goals is to fit the location of a delta function line profile under a model-based Bayesian statistical perspective.
The photon counts collected by Chandra are convolved with various factors such as absorption, effective area, instrument response, and background contamination; this necessitates accounting for the data generation mechanism within a spectral model. Bayesian methods offer a straightforward way of handling the complexity of Chandra data. When Gaussian functions are used to model the spectral lines, the standard Bayesian missing data algorithms are readily available to solve the problem; see van Dyk et al. (2001) for details. However, the use of the delta function line profile gives rise to computational challenges requiring the use of state-of-the-art statistical algorithms. Here, we discuss the implementation of each statistical algorithm, and we illustrate how to apply the algorithms to a highly structured multilevel spectral model with an analysis of the energy spectrum of the high redshift quasar, PG1634+706. The authors gratefully acknowledge funding for this project partially provided by NSF grant DMS-01-04129 and by NASA Contract NAS8-39073 (Chandra X-ray Center).
Park Tuson
Siemiginowska Aneta
van Dyk David
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