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We show that in the continuum limit, the average spectrum method (ASM) isequivalent to maximizing R\'enyi entropies of order $\eta$, of which Shannonentropy is the special case $\eta=1$. The order of R\'enyi entropy isdetermined by the way the spectra are sampled. Our derivation also suggests amodification of R\'enyi entropy, giving it a non-trivial $\eta\to0$ limit. Weshow that the sharper peaks generally obtained in ASM are associated withentropies of order $\eta<1$. Our work provides a generalization of the maximumentropy method that enables extracting more structure than the traditionalmethod.

Generalized Maximum Entropy Methods as Limits of the Average Spectrum Method