Comment on "Inference with minimal Gibbs free energy in information field theory"

Iatsenko, D. and Stefanovska, A. and McClintock, P. V. E. (2012) Comment on "Inference with minimal Gibbs free energy in information field theory". Physical Review E, 85 (3). -. ISSN 1539-3755

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Abstract

Ensslin and Weig [Phys. Rev. E 82, 051112 (2010)] have introduced a "minimum Gibbs free energy" (MGFE) approach for estimation of the mean signal and signal uncertainty in Bayesian inference problems: it aims to combine the maximum a posteriori (MAP) and maximum entropy (ME) principles. We point out, however, that there are some important questions to be clarified before the new approach can be considered fully justified, and therefore able to be used with confidence. In particular, after obtaining a Gaussian approximation to the posterior in terms of the MGFE at some temperature T, this approximation should always be raised to the power of T to yield a reliable estimate. In addition, we show explicitly that MGFE indeed incorporates the MAP principle, as well as the MDI (minimum discrimination information) approach, but not the well-known ME principle of Jaynes [E.T. Jaynes, Phys. Rev. 106, 620 (1957)]. We also illuminate some related issues and resolve apparent discrepancies. Finally, we investigate the performance of MGFE estimation for different values of T, and we discuss the advantages and shortcomings of the approach.

Item Type: Journal Article
Journal or Publication Title: Physical Review E
Additional Information: ©2012 American Physical Society
Uncontrolled Keywords: /dk/atira/pure/researchoutput/libraryofcongress/qc
Subjects:
Departments: Faculty of Science and Technology > Physics
ID Code: 54942
Deposited By: ep_importer_pure
Deposited On: 07 Jun 2012 14:10
Refereed?: Yes
Published?: Published
Last Modified: 28 Feb 2020 01:37
URI: https://eprints.lancs.ac.uk/id/eprint/54942

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