A path integral approach to Bayesian inference in Markov processes

TL;DR

This paper introduces a novel method for Bayesian inference in Markov processes using path integral techniques, connecting it to quantum mechanics through an imaginary-time Schrödinger equation with likelihood as a potential.

Contribution

It formulates Bayesian updates in Markov processes via path integrals and derives a Schrödinger-like equation incorporating likelihood as a potential.

Findings

Provides a new mathematical framework for Bayesian inference in Markov processes.

Establishes a connection between Bayesian updates and quantum mechanics.

Enables potential new computational methods for inference.

Abstract

We formulate Bayesian updates in Markov processes by means of path integral techniques and derive the imaginary-time Schr\"{o}dinger equation with likelihood to direct the inference incorporated as a potential for the posterior probability distribution