Journal Article

A comparison of frequentist and Bayesian inference: searching for low-frequency p modes and g modes in Sun-as-a-star data

A.-M. Broomhall, W. J. Chaplin, Y. Elsworth, T. Appourchaux and R. New

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 406, issue 2, pages 767-781
Published in print August 2010 | ISSN: 0035-8711
Published online July 2010 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2010.16743.x
A comparison of frequentist and Bayesian inference: searching for low-frequency p modes and g modes in Sun-as-a-star data

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We describe and use two different statistical approaches to try and detect low-frequency solar oscillations in Sun-as-a-star data: a frequentist approach and a Bayesian approach. We have used frequentist statistics to search contemporaneous Sun-as-a-star data for coincident, statistically prominent features. However, we find that this approach leads to numerous false detections. We have also used Bayesian statistics to search for evidence of low-frequency p modes and g modes in Sun-as-a-star data. We describe how Bayesian statistics can be used to search near-contemporaneous data for coincident prominent features. Near-contemporaneous data were used to circumvent the difficulties in deriving probabilities that occur when common noise is present in the data. We find that the Bayesian approach, which is reliant on the assumptions made when determining the posterior probability, leads to significantly fewer false detections and those that are observed can be discredited using a priori knowledge. Therefore, we have more confidence in the mode candidates found with Bayesian statistics.

Keywords: methods: data analysis; methods: statistical; Sun: helioseismology; Sun: oscillations

Journal Article.  12794 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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