Maximum Entropy

The maximum entropy principle is a rule for assigning probability distributions that demands one select the distribution consistent with known constraints — mean values, variance bounds, support restrictions — that has the highest entropy, meaning the distribution that makes the fewest additional assumptions beyond what is already known. Developed by E. T. Jaynes as an extension of objective Bayesian methods, the principle treats entropy not as a property of physical systems but as a measure of informational ignorance, and it claims that maximizing entropy under constraints is the unique logically consistent way to represent partial knowledge. The principle has been applied across statistical mechanics, image reconstruction, natural language processing, and ecological inference, though critics argue that the choice of constraints is itself subjective and that the principle's mathematical elegance conceals a covert dependence on the representation of the problem. Whether maximum entropy is a genuine method of objective inference or a sophisticated way of hiding assumptions remains one of the persistent fault lines in the philosophy of probability.