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The Detection Problem | |
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The ability to determine whether data contains just instrument noise, or noise plus a resolvable gravitational wave signal,
is the central problem in gravitational wave astronomy. The “detection problem” can be divided into three stages:
Search, characterization, and evaluation. The search phase is where we find the best fit configuration for the hypothesis under
consideration. Characterization is where we determine how well (or poorly) constrained this fit is. The final evaluation
phase compares this hypothesis to others under consideration. To do all of this we have created an algorithm that, for the first
time, solves all three phases of the detection problem. We do so with an approach which relies solely on Bayesian
probability theory.
Bayesian methods offer a unique way of reaching a reliable conclusion about a marginal result. The work horse of many Bayesian approaches to data analysis problems is the Markov Chain Monte Carlo family of algorithms. These methods have shown promise in solving many of the most complex data analysis challenges that are faced by current and future GW detectors. |
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The image to the left is the sort of thing that keeps me up at night. It shows the confidence one can have in a candidate detection as a function of its signal to noise ratio. The different lines represent different noise realizations (with identicle noise characteristics) competing against the same source. What we discovered is how (logically) the detectability of a source strongly depends on the specific noise within which that source is burried. This effect is significant enough to justify the use of Bayesian methods in all such applications, as they are solely sensitive to such specifics regarding the data. |
| This example was accomplished using simulated LISA data, which poses significantly simpler noise modeling than does the ground based effort. Our current work is in extending this algorithm to handle the inescapable unpleasentries found in LIGO data. | |
| Publications | |
| “Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy” | |
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N.J. Cornish and T.B. Littenberg, Phys. Rev. D76, 083006 (2007). |
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| “Resolving Model Selection Problems in Gravitational Wave Astronomy” | |
| T.B. Littenberg and N.J. Cornish, GWDAW 12 Poster (2007). | |
| “A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy” | |
| T.B. Littenberg and N.J. Cornish, arXiv:0902.0368 [gr-qc] (2009). | |
Montana State University
Bozeman, MT 59717
406.994.1677
littenberg@physics.montana.edu