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

Details Comment on ``Inference with minimal Gibbs free energy in information field theory'' Comment on ``Inference with minimal Gibbs free energy in information field theory''

Mar 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012phrve..85c3101i&link_type=abstract

Physical Review E, vol. 85, Issue 3, id. 033101

Computer Science

Performance

1

Information And Communication Theory, Field Theory, Observational Cosmology, Image Processing

Scientific paper

Enßlin and Weig [Phys. Rev. E1539-375510.1103/PhysRevE.82.051112 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.PHRVAO0031-899X10.1103/PhysRev.106.620 106, 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.

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