Reply to “Comment on ‘Inference with minimal Gibbs free energy in information field theory’ ”

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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.

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