A non-parametric ensemble transform method for Bayesian inference

TL;DR

This paper introduces a novel non-parametric ensemble transform approach for Bayesian inference that leverages optimal transportation, avoiding assumptions inherent in traditional methods like EnKFs.

Contribution

The paper presents a new ensemble transform method based on optimal transportation, which is non-parametric and does not rely on linear regression assumptions.

Findings

The proposed method is robust for small ensemble sizes.

It does not rely on prior assumptions about distributions.

It offers a consistent alternative to existing Bayesian inference methods.

Abstract

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a prior assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.