Generalized maximum entropy methods as limits of the average spectrum method

We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing Renyi entropies of order eta, of which Shannon entropy is the special case eta = 1. The order of Renyi entropy is determined by the way the spectra are sampled. Our derivation also suggests a modification of Renyi entropy, giving it a nontrivial eta -> 0 limit. We show that the sharper peaks generally obtained in ASM are associated with entropies of order eta < 1. Our paper provides a generalization of the maximum entropy method that enables extracting more structure than the traditional method.