"Negative probabilities" as relative probabilistic expressions

TL;DR

This paper explores the concept of negative probabilities as a natural extension of probabilistic expressions, providing operational interpretations and demonstrating practical benefits such as more memory-efficient stochastic simulation algorithms.

Contribution

It introduces a framework for understanding negative probabilities as relative probabilistic expressions with operational meaning, leading to improved simulation algorithms.

Findings

Negative probabilities can be given an operational interpretation.

Negative probabilities can be used to develop more memory-efficient algorithms.

The ideas have practical applications in stochastic simulations.

Abstract

Here we briefly discuss how negative numbers, or "negative probabilities", can naturally arise in probabilistic expressions and be given an operational interpretation. Like the use of negative numbers in arithmetical expressions, the use of negative probabilities can have substantial practical value. Indeed, some of the ideas discussed here have led to stochastic simulation algorithms that require much less memory than the best classical algorithms known to date [arXiv:1906.00263].