Mathematics – Probability
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aas...209.7812c&link_type=abstract
2007 AAS/AAPT Joint Meeting, American Astronomical Society Meeting 209, #78.12; Bulletin of the American Astronomical Society, V
Mathematics
Probability
Scientific paper
The Aromatic Infrared Bands (AIBs) are prominent features of many galactic spectra in the infrared and are strongly associated with star-forming regions. Polycyclic Aromatic Hydrocarbons (PAHs) are a leading contender as the source for this emission. Unequivocally establishing this identification has been difficult since the AIBs do not appear to be the result of emission from a small, tractable number of PAHs. Rather the observed emission bands appear to be composed of the contributions from possibly hundreds of different PAHs, neutral and ionized, each with its own distinctive spectrum. A major step toward verifying the PAH hypothesis would be to quantitatively establish how well the observed AIBs can be explained, or not explained, as the combination of known PAH spectra. To date this problem has been attacked by either manually superimposing individual PAH spectra or by using non-negative least squares. We explain how both of these approaches have serious deficiencies.
We then describe our progress in applying Bayesian source separation techniques to this difficult problem. In this phase of our investigation, we have worked with theoretically generated PAH spectra at a single temperature composed of combinations of arbitrarily selected PAHs with added Gaussian noise. First, we show how the non-negative least squares approach fares as a function of PAH composition, noise level, and spectral resolution. Next, we outline our Bayesian approach, which relies on Skilling's nested sampling algorithm. This approach allows us to find highly probable solutions and evaluate the uncertainties in our estimates by sampling the posterior. Moreover, this algorithm also enables us to compute the evidence provided by the data as well as visualize the posterior probability in the high-dimensional hypothesis space generated by the numerous combinations of possible PAH contributions.
This research is supported by NASA Applied Information Systems Research Grant 05-AISR05-0143.
Carbon Duane F.
Knuth Kevin H.
Tse M. K.
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