Bayesian and Maximum Entropy Methods

The Bayesian and Maximum Entropy Methods are now standard routines in various data analyses, irrespective of ones own preference to the more conventional approach based on so-called frequentists understanding of the notion of the probability. It is not the purpose of the Editor to show all achievements of these methods in various branches of science, technology and medicine. In the case of condensed matter physics most of the oldest examples of Bayesian analysis can be found in the excellent tutorial textbooks by Sivia and Skilling [1], and Bretthorst [2], while the application of the Maximum Entropy Methods were described in 'Maximum Entropy in Action' [3]. On the list of questions addressed one finds such problems as deconvolution and reconstruction of the complicated spectra, e.g. counting the number of lines hidden within the spectrum observed with always finite resolution, reconstruction of charge, spin and momentum density distribution from an incomplete sets of data, etc. On the theoretical side one might find problems like estimation of interatomic potentials [4], application of the MEM to quantum Monte Carlo data [5], Bayesian approach to inverse quantum statistics [6], very general to statistical mechanics [7] etc. Obviously, in spite of the power of the Bayesian and Maximum Entropy Methods, it is not possible for everything to be solved in a unique way by application of these particular methods of analysis, and one of the problems which is often raised is connected not only with a uniqueness of a reconstruction of a given distribution (map) but also with its accuracy (error maps). In this 'Comments' section we present a few papers showing more recent advances and views, and highlighting some of the aforementioned problems.