Twenty-five years of maximum-entropy principle

The strengths and weaknesses of the maximum entropy principle (MEP) are examined and some challenging problems that remain outstanding at the end of the first quarter century of the principle are discussed. The original formalism of the MEP is presented and its relationship to statistical mechanics is set forth. The use of MEP for characterizing statistical distributions, in statistical inference, nonlinear spectral analysis, transportation models, population density models, models for brand-switching in marketing and vote-switching in elections is discussed. Its application to finance, insurance, image reconstruction, pattern recognition, operations research and engineering, biology and medicine, and nonparametric density estimation is considered.