34th Solar Physics Division Meeting, June 2003
Session 2 Data Analysis Challenges I
Oral, Monday, June 16, 2003, 1:30-3:30pm, Auditorium

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[2.01] A Response Matrix Approach to the Reconstruction of Differential Emission Measure

H. Kang, D. A. van Dyk (Department of Statistics, Harvard University), A. Connors (Eurika Scientific), V. Kashyap (Harvard-Smithsonian Center for Astrophysics), Harvard-Smithsonian Astrostatistics Group Collaboration

The differential emission measure (DEM) provides a powerful tool for the characterization of the temperature structure of a stellar atmosphere. In this talk we develop a new method for the reconstruction of a DEM distribution within a Bayesian framework. In particular, we use a ``response matrix" to map from the unobserved photon counts in a number of temperature bins to the spectral line counts. This requires high resolution data and the resolution of many spectral lines that we obtain using Chandra gratings. Numerically, to reconstruct the unobserved counts in the temperature bins we must solve a difficult problem, which we accomplish using the method of data augmentation. Specifically we treat the counts for each temperature bin as ``missing data". Under this construction, we are able to use statistical methods that are designed to handle missing data problems. In particular, we use the Expectation-Maximization (EM) and Markov chain Monte Carlo (MCMC) methods, which allow us to find the maximum a postriori estimates and the highest posterior density intervals to construct estimates and error bars. We implement a Bayesian multiscale (wavelet-like) model to smooth the DEM distribution, which gives us the flexibility to overcome the lack of information especially with low count data. This approach allows for global spectral modeling, with the ability to include prior information in the form of known sequences and relative strengths of lines; the inclusion and propagation of errors in atomic data; and a proper accounting of the uncertainties in the reconstructed DEM. We provide several simulation studies with both high-count and low-count data to evaluate the proposed method.

The authors gratefully acknowledge funding for this project partially provided by NSF grant DMS-01-04129 and by NASA contract NAS8-39073 (CXC).


If you would like more information about this abstract, please follow the link to http://www.fas.harvard.edu/~vandyk/astrostat.html. This link was provided by the author. When you follow it, you will leave the Web site for this meeting; to return, you should use the Back comand on your browser.

The author(s) of this abstract have provided an email address for comments about the abstract: kang@stat.harvard.edu

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