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Brandon Kelly University of California, Santa Barbara

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"Astronomical Application of a Nonlinear Random Effects Model with Multiplicative Measurement Error"
12 January 2012 from 4:00 PM to 5:00 PM
201 Thomas Bldg.
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Many data analysis problems in astronomy can be structured within the context of nonlinear random effects models. In this talk I discuss an astronomical application of a nonlinear random effects model which also has a multiplicative measurement error term due to instrument calibration. The goal of this application is to use observations from recent space-based telescopes, such as Herschel and Planck, to study the properties of dust in regions currently forming stars. I discuss a Bayesian analysis of this problem, and contrast it with the traditional least-squares methods commonly used in the astronomical literature. The inclusion of a multiplicative measurement error creates extremely slow convergence of a Gibbs sampler under the standard data augmentation. To make the MCMC sampler more efficient I discuss the implementation of an ancillarity-sufficiency interweaving strategy which incorporates an alternative data augmentation. I show that for this particular astronomical application the results obtained using the nonlinear random effects model lead to scientific conclusions which are opposite those obtained through the traditional least-squares analysis, but are consistent with the scientific expectations. Finally, I conclude with a discussion of directions for future work on nonlinear random effects models motivated by astronomical applications, and the need for such models in analyzing data from current and future astronomical facilities.

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