A framework for general discrete probability calculations

Abstract

Probability follows a simple and concise set of rules. In practice, however, reason- ing about probability may be highly unintuitive and this leads to the possibility of miscalculations even for simple problems. We present an approach to facilitate the correct description of systems governed by discrete probability. The methods described in this paper allow making general statements about the values of prob- ability. This information can next be used to calculate any probability related to the system described by the statements. In case there are too few statements to provide a unique answer, entropy maximization is used to fill in the miss- ing information. The approach has wide potential applications that range from experimental physics to natural language analysis. The theoretical framework described here is also the basis of a software implementation that is designed to be straightforward to extend and requires only popular python libraries, numpy, torch, sympy, and scipy.