Cluster Sampling Filters for Non-Gaussian Data Assimilation
Abstract
This paper presents a fully non-Gaussian filter for sequential data assimilation. The filter is named the “cluster sampling filter”, and works by directly sampling the posterior distribution following a Markov Chain Monte-Carlo (MCMC) approach, while the prior distribution is approximated using a Gaussian Mixture Model (GMM). Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a GMM to the prior ensemble. Using the data likelihood function, the posterior density is then formulated as a mixture density, and is sampled following an MCMC approach. Four versions of the proposed filter, namely C ℓ MCMC , C ℓ HMC , MC- C ℓ HMC , and MC- C ℓ HMC are presented. C ℓ MCMC uses a Gaussian proposal density to sample the posterior, and C ℓ HMC is an extension to the Hamiltonian Monte-Carlo (HMC) sampling filter. MC- C ℓ MCMC and MC- C ℓ HMC are multi-chain versions of the cluster sampling filters C ℓ MCMC and C ℓ HMC respectively. The multi-chain versions are proposed to guarantee that samples are taken from the vicinities of all probability modes of the formulated posterior. The new methodologies aremore »
- Authors:
-
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- Air Force Research Laboratory (AFRL), Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF); Virginia Polytechnic Institute, Dept of Computer Science; USDOE
- OSTI Identifier:
- 1463676
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Atmosphere (Basel)
- Additional Journal Information:
- Journal Name: Atmosphere (Basel); Journal Volume: 9; Journal Issue: 6; Journal ID: ISSN 2073-4433
- Publisher:
- MDPI
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; data assimilation; ensemble filters; gaussian mixture models; hamiltonian monte-carlo; markov chain monte-carlo sampling
Citation Formats
Attia, Ahmed, Moosavi, Azam, and Sandu, Adrian. Cluster Sampling Filters for Non-Gaussian Data Assimilation. United States: N. p., 2018.
Web. doi:10.3390/atmos9060213.
Attia, Ahmed, Moosavi, Azam, & Sandu, Adrian. Cluster Sampling Filters for Non-Gaussian Data Assimilation. United States. https://doi.org/10.3390/atmos9060213
Attia, Ahmed, Moosavi, Azam, and Sandu, Adrian. Thu .
"Cluster Sampling Filters for Non-Gaussian Data Assimilation". United States. https://doi.org/10.3390/atmos9060213. https://www.osti.gov/servlets/purl/1463676.
@article{osti_1463676,
title = {Cluster Sampling Filters for Non-Gaussian Data Assimilation},
author = {Attia, Ahmed and Moosavi, Azam and Sandu, Adrian},
abstractNote = {This paper presents a fully non-Gaussian filter for sequential data assimilation. The filter is named the “cluster sampling filter”, and works by directly sampling the posterior distribution following a Markov Chain Monte-Carlo (MCMC) approach, while the prior distribution is approximated using a Gaussian Mixture Model (GMM). Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a GMM to the prior ensemble. Using the data likelihood function, the posterior density is then formulated as a mixture density, and is sampled following an MCMC approach. Four versions of the proposed filter, namely C ℓ MCMC , C ℓ HMC , MC- C ℓ HMC , and MC- C ℓ HMC are presented. C ℓ MCMC uses a Gaussian proposal density to sample the posterior, and C ℓ HMC is an extension to the Hamiltonian Monte-Carlo (HMC) sampling filter. MC- C ℓ MCMC and MC- C ℓ HMC are multi-chain versions of the cluster sampling filters C ℓ MCMC and C ℓ HMC respectively. The multi-chain versions are 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 simple one-dimensional example, and a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Here, numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption especially in the HMC filtering paradigm.},
doi = {10.3390/atmos9060213},
journal = {Atmosphere (Basel)},
number = 6,
volume = 9,
place = {United States},
year = {Thu May 31 00:00:00 EDT 2018},
month = {Thu May 31 00:00:00 EDT 2018}
}
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Works referencing / citing this record:
Tuning Covariance Localization Using Machine Learning
book, June 2019
- Moosavi, Azam; Attia, Ahmed; Sandu, Adrian
- Computational Science – ICCS 2019: 19th International Conference, Faro, Portugal, June 12–14, 2019, Proceedings, Part IV, p. 199-212