# Particle Flow Bayes' Rule

## TL;DR

This paper introduces a neural ODE-based particle flow method for Bayesian inference that generalizes across different priors and observations, enabling efficient sequential Bayesian updates.

## Contribution

It presents a novel neural ODE operator for particle flow Bayes' rule, capable of generalizing across various priors and observations, trained via meta-learning.

## Key findings

- Successfully applied to high-dimensional examples
- Demonstrated generalization across different priors and observations
- Proved the existence of the neural ODE operator

## Abstract

We present a particle flow realization of Bayes' rule, where an ODE-based neural operator is used to transport particles from a prior to its posterior after a new observation. We prove that such an ODE operator exists. Its neural parameterization can be trained in a meta-learning framework, allowing this operator to reason about the effect of an individual observation on the posterior, and thus generalize across different priors, observations and to sequential Bayesian inference. We demonstrated the generalization ability of our particle flow Bayes operator in several canonical and high dimensional examples.