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Segmented Nonparametric Models of Distributed Data: From Photons to Galaxies
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| A novel technique, and an efficient algorithm to implement it, provides piecewise-constant models for a variety of one dimensional data types common in high energy astrophysics and cosmology, as well as in physical simulations of astrophysical systems. We will improve this algorithm in various ways (speed, parameter selection, alternative fitness functions, etc.) However, the major task will be extension of this methodology to 2D data (such as galaxy surveys), 3D data (redshift surveys), and higher dimensional data spaces. We have recently discovered a way to transform higher dimensional problems into approximately equivalent 1D cases, solvable with the 1D algorithm. A major mathematical goal of this work is to find rigorous solutions in higher dimensions. We will simultaneously derive scientifically important results and hone the methods on analysis of GLAST photon maps, 3D galaxy positions derived from redshift surveys, and stellar infrared data useful for detection of molecular clouds. Ultimately these methods will be applicable to a wide range of astrophysical problems. |
Bibliography
| | An algorithm for optimal partitioning of data on an interval
Jackson, Brad; Scargle; Jeffrey; Barnes, Arabhi, Alt, Gioumousis, Gwin, Sangtrakulcharoen, Tan and Tsai, IEEE Signal Processing Letters, (Feb., 2005) 12 pp. 105-108
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