Subjectivity in Application of the Principle of Maximum Entropy

Abstract

Complete prior statistical information is currently required in the majority of statistical evaluations of complex models. The principle of maximum entropy is often utilized in this context to fill in the missing pieces of available information and is normally claimed to be fair and objective. A rarely discussed aspect is that it relies upon testable information, which is never known but estimated, i.e . results from processing of raw data. The subjective choice of this processing strongly affects the result. Less conventional posterior completion of information is equally accurate but is computationally superior to prior, as much less information enters the analysis. Our recently proposed methods of lean deterministic sampling are examples of very few approaches that actively promote the use of minimal incomplete prior information. The inherited subjective character of maximum entropy distributions and the often critical implications of prior and posterior completion of information are here discussed and illustrated, from a novel perspective of consistency, rationality, computational efficiency and realism.