On the detection of Lorentzian profiles in a power spectrum: a Bayesian approach using ignorance priors

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dc.creator Guenther, David B.
dc.creator Gruberbauer, Michael
dc.creator Kallinger, T.
dc.creator Weiss, W. W.
dc.date.accessioned 2015-03-02T16:33:33Z
dc.date.available 2015-03-02T16:33:33Z
dc.date.issued 2009-11
dc.identifier.issn 1432-0746
dc.identifier.issn 0004-6361
dc.identifier.uri http://library2.smu.ca/xmlui/handle/01/25967
dc.description Publisher's version/PDF en_CA
dc.description.abstract Aims. Deriving accurate frequencies, amplitudes, and mode lifetimes from stochastically driven pulsation is challenging, more so, if one demands that realistic error estimates be given for all model fitting parameters. As has been shown by other authors, the traditional method of fitting Lorentzian profiles to the power spectrum of time-resolved photometric or spectroscopic data via the maximum likelihood estimation (MLE) procedure delivers good approximations for these quantities. We, however, show that a conservative Bayesian approach allows one to treat the detection of modes with minimal assumptions (i.e., about the existence and identity of the modes). Methods. We derive a conservative Bayesian treatment for the probability of Lorentzian profiles being present in a power spectrum and describe an efficient implementation that evaluates the probability density distribution of parameters by using a Markov-chain Monte Carlo (MCMC) technique. Results. Potentially superior to “best-fit” procedure like MLE, which only provides formal uncertainties, our method samples and approximates the actual probability distributions for all parameters involved. Moreover, it avoids shortcomings that make the MLE treatment susceptible to the built-in assumptions of a model that is fitted to the data. This is especially relevant when analyzing solar-type pulsation in stars other than the Sun where the observations are of lower quality and can be over-interpreted. As an example, we apply our technique to CoRoT observations of the solar-type pulsator HD 49933. en_CA
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dc.language.iso en en_CA
dc.publisher EDP Sciences en_CA
dc.relation.uri http://dx.doi.org/10.1051/0004-6361/200811203
dc.rights Article is made available in accordance with the publisher’s policy and is subject to copyright law. Please refer to the publisher’s site. Any re-use of this article is to be in accordance with the publisher’s copyright policy. This posting is in no way granting any permission for re-use to the reader/user.
dc.subject.lcsh Stellar oscillations
dc.subject.lcsh Statistical astronomy
dc.title On the detection of Lorentzian profiles in a power spectrum: a Bayesian approach using ignorance priors en_CA
dc.type Text en_CA
dcterms.bibliographicCitation Astronomy & Astrophysics 506, 1043-1053. (2009) en_CA
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Article is made available in accordance with the publisher’s policy and is subject to copyright law. Please refer to the publisher’s site. Any re-use of this article is to be in accordance with the publisher’s copyright policy. This posting is in no way granting any permission for re-use to the reader/user.
 
Published Version: http://dx.doi.org/10.1051/0004-6361/200811203
 
 

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