Cluster Sampling Filters for Non-Gaussian Data Assimilation
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.
Cite
@article{arxiv.1607.03592,
title = {Cluster Sampling Filters for Non-Gaussian Data Assimilation},
author = {Ahmed Attia and Azam Moosavi and Adrian Sandu},
journal= {arXiv preprint arXiv:1607.03592},
year = {2016}
}