A MAXIMUM-ENTROPY METHOD WITH A-PRIORI MAXIMUM-LIKELIHOOD CONSTRAINTS

Implementations of the maximum entropy method for data reconstruction have almost universally used the approach of maximizing the statistic S - lambda chi(2), where S is the Shannon entropy of the reconstructed distribution and chi(2) is the usual statistical measure associated w ith agreement between certain properties of the reconstructed distribu tion and the data. We develop here an alternative approach which maxim izes the entropy subject to the set of constraints that chi(2) be at a minimum with respect to the reconstructed distribution. This in turn modifies the fitting statistic to be S - lambda .del chi(2) where lamb da is now a vector. This new method provides a unique solution to both the well-posed and ill-posed problem, provides a natural convergence criterion which has previously been lacking in other implementations o f maximum entropy, and provides the most conservative (least informati ve) data reconstruction result consistent with both maximum entropy an d maximum likelihood methods, thereby mitigating against overinterpret ation of reconstruction results. A spectroscopic example is shown as a demonstration.