Overcoming the Artificial Biases for the Nonadditive $ q $-Entropy

TL;DR

This paper addresses the artificial biases introduced when using nonadditive $q$-entropy with entropy maximization, proposing a method that considers its discrete structure to improve the inference of probability distributions.

Contribution

It introduces a novel approach that accounts for the discrete structure of $q$-entropy, overcoming biases and enhancing the understanding of Jaynes' entropy maximization.

Findings

Artificial biases in $q$-entropy maximization are mitigated.

Considering the discrete structure improves probability inference.

The approach clarifies the entropy maximization process for nonadditive entropies.

Abstract

Entropy maximization procedure has been a general practice in many diverse fields of science to obtain the concomitant probability distributions. The consistent use of the maximization procedure on the other hand requires the probability distributions to obey the probability multiplication rule for independent events. However, despite that the nonadditive $ q $-entropy is known not to obey this rule, it is still used with the entropy maximization procedure to infer the probability distributions at the expense of creating artificial biases not present in the data itself. Here we show that this important obstacle can be overcome by considering the intrinsic discrete structure and related averaging scheme of the nonadditive $ q $-entropy. This also paves the road to a better understanding of the entropy maximization procedure of Jaynes.