Reply to "Comment on `Inference with minimal Gibbs free energy in information field theory'" by Iatsenko, Stefanovska and McClintock

TL;DR

This paper clarifies the minimal Gibbs free energy approach in information field theory, addressing controversies about signal estimation and uncertainty inference, and distinguishes between related entropy concepts.

Contribution

It clarifies the application of Gibbs free energy in signal inference and distinguishes between maximum entropy principles and methods.

Findings

The approach's core remains unaffected by the comment.

Extending the method for uncertainty inference requires undoing posterior tempering.

Clarifies differences between maximum entropy concepts.

Abstract

We endorse the comment on our recent paper [En{\ss}lin and Weig, Phys. Rev. E 82, 051112 (2010)] by Iatsenko, Stefanovska and McClintock [Phys. Rev. E 85 033101 (2012)] and we try to clarify the origin of the apparent controversy on two issues. The aim of the minimal Gibbs free energy approach to provide a signal estimate is not affected by their Comment. However, if one wants to extend the method to also infer the a posteriori signal uncertainty any tempering of the posterior has to be undone at the end of the calculations, as they correctly point out. Furthermore, a distinction is made here between maximum entropy, the maximum entropy principle, and the so-called maximum entropy method in imaging, hopefully clarifying further the second issue of their Comment paper.