Cluster Sampling Filters for Non-Gaussian Data Assimilation

TL;DR

This paper introduces a non-Gaussian data assimilation filter that uses Gaussian Mixture Models and Hamiltonian Monte Carlo sampling, improving the ability to handle multimodal and non-Gaussian prior distributions in high-dimensional systems.

Contribution

It develops the cluster HMC sampling filter (ClHMC) and its multi-chain version (MC-ClHMC), relaxing the Gaussian prior assumption in HMC filtering and enabling better sampling of complex posterior distributions.

Findings

GMMs effectively relax Gaussian prior assumptions.

ClHMC accurately captures multimodal posteriors.

Numerical tests show improved data assimilation performance.

Abstract

This paper presents a fully non-Gaussian version of the Hamiltonian Monte Carlo (HMC) sampling filter. The Gaussian prior assumption in the original HMC filter is relaxed. Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a Gaussian Mixture Model (GMM) to the prior ensemble. Using the data likelihood function, the posterior density is then formulated as a mixture density, and is sampled using a HMC approach (or any other scheme capable of sampling multimodal densities in high-dimensional subspaces). The main filter developed herein is named "cluster HMC sampling filter" (ClHMC). A multi-chain version of the ClHMC filter, namely MC-ClHMC is also proposed to guarantee that samples are taken from the vicinities of all probability modes of the formulated posterior. The new methodologies are tested using a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption in the HMC filtering paradigm.