Comparison of numerical approaches to Bayesian updating

Bojana Rosić; Jan Sýkora; Oliver Pajonk; Anna Kučerová; Hermann G. Matthies

doi:10.1007/978-3-319-27996-1_16

Comparison of numerical approaches to Bayesian updating

Bojana Rosić^*, Jan Sýkora, Oliver Pajonk, Anna Kučerová, Hermann G. Matthies

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

8 Citations (Scopus)

Abstract

This paper investigates the Bayesian process of identifying unknown model parameters given prior information and a set of noisy measurement data. There are two approaches being adopted in this research: one that uses the classical formula for measures and probability densities and one that leaves the underlying measure unchanged and updates the relevant random variable. The former is numerically tackled by a Markov chain Monte Carlo procedure based on the Metropolis- Hastings algorithm, whereas the latter is implemented via the ensemble/square root ensemble Kalman filters, as well as the functional approximation approaches in the form of the polynomial chaos based linear Bayesian filter and its corresponding square root algorithm. The study attempts to show the principal differences between full and linear Bayesian updates when a direct or a transformed version of measurements are taken into consideration. In this regard the comparison of both strategies is provided on the example of a steady state diffusion equation with nonlinear and transformed linear measurement operators.

Original language	English
Title of host publication	Computational Methods for Solids and Fluids
Subtitle of host publication	Multiscale Analysis, Probability Aspects and Model Reduction
Editors	Adnan Ibrahimbegovic
Place of Publication	Cham
Publisher	Springer
Pages	427-461
Number of pages	35
ISBN (Electronic)	978-3-319-27996-1
ISBN (Print)	978-3-319-27994-7
DOIs	https://doi.org/10.1007/978-3-319-27996-1_16
Publication status	Published - 1 Jan 2016
Externally published	Yes
Event	2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015 - Sarajevo, Bosnia and Herzegovina Duration: 10 Jun 2015 → 12 Jun 2015 Conference number: 2

Publication series

Name	Computational Methods in Applied Sciences
Publisher	Springer
Volume	41
ISSN (Print)	1871-3033

Conference

Conference	2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015
Country/Territory	Bosnia and Herzegovina
City	Sarajevo
Period	10/06/15 → 12/06/15

Keywords

Ensemble Kalman filter
Markov chain Monte Carlo
Polynomial chaos based linear Bayesian update
Square root algorithm

Access to Document

10.1007/978-3-319-27996-1_16

Cite this

Rosić, B., Sýkora, J., Pajonk, O., Kučerová, A., & Matthies, H. G. (2016). Comparison of numerical approaches to Bayesian updating. In A. Ibrahimbegovic (Ed.), Computational Methods for Solids and Fluids: Multiscale Analysis, Probability Aspects and Model Reduction (pp. 427-461). (Computational Methods in Applied Sciences; Vol. 41). Springer. https://doi.org/10.1007/978-3-319-27996-1_16

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title = "Comparison of numerical approaches to Bayesian updating",

abstract = "This paper investigates the Bayesian process of identifying unknown model parameters given prior information and a set of noisy measurement data. There are two approaches being adopted in this research: one that uses the classical formula for measures and probability densities and one that leaves the underlying measure unchanged and updates the relevant random variable. The former is numerically tackled by a Markov chain Monte Carlo procedure based on the Metropolis- Hastings algorithm, whereas the latter is implemented via the ensemble/square root ensemble Kalman filters, as well as the functional approximation approaches in the form of the polynomial chaos based linear Bayesian filter and its corresponding square root algorithm. The study attempts to show the principal differences between full and linear Bayesian updates when a direct or a transformed version of measurements are taken into consideration. In this regard the comparison of both strategies is provided on the example of a steady state diffusion equation with nonlinear and transformed linear measurement operators.",

keywords = "Ensemble Kalman filter, Markov chain Monte Carlo, Polynomial chaos based linear Bayesian update, Square root algorithm",

author = "Bojana Rosi{\'c} and Jan S{\'y}kora and Oliver Pajonk and Anna Ku{\v c}erov{\'a} and Matthies, {Hermann G.}",

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doi = "10.1007/978-3-319-27996-1_16",

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Rosić, B, Sýkora, J, Pajonk, O, Kučerová, A & Matthies, HG 2016, Comparison of numerical approaches to Bayesian updating. in A Ibrahimbegovic (ed.), Computational Methods for Solids and Fluids: Multiscale Analysis, Probability Aspects and Model Reduction. Computational Methods in Applied Sciences, vol. 41, Springer, Cham, pp. 427-461, 2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015, Sarajevo, Bosnia and Herzegovina, 10/06/15. https://doi.org/10.1007/978-3-319-27996-1_16

Comparison of numerical approaches to Bayesian updating. / Rosić, Bojana; Sýkora, Jan; Pajonk, Oliver et al.
Computational Methods for Solids and Fluids: Multiscale Analysis, Probability Aspects and Model Reduction. ed. / Adnan Ibrahimbegovic. Cham: Springer, 2016. p. 427-461 (Computational Methods in Applied Sciences; Vol. 41).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Rosić, Bojana

AU - Sýkora, Jan

AU - Pajonk, Oliver

AU - Kučerová, Anna

AU - Matthies, Hermann G.

N1 - Conference code: 2

PY - 2016/1/1

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N2 - This paper investigates the Bayesian process of identifying unknown model parameters given prior information and a set of noisy measurement data. There are two approaches being adopted in this research: one that uses the classical formula for measures and probability densities and one that leaves the underlying measure unchanged and updates the relevant random variable. The former is numerically tackled by a Markov chain Monte Carlo procedure based on the Metropolis- Hastings algorithm, whereas the latter is implemented via the ensemble/square root ensemble Kalman filters, as well as the functional approximation approaches in the form of the polynomial chaos based linear Bayesian filter and its corresponding square root algorithm. The study attempts to show the principal differences between full and linear Bayesian updates when a direct or a transformed version of measurements are taken into consideration. In this regard the comparison of both strategies is provided on the example of a steady state diffusion equation with nonlinear and transformed linear measurement operators.

AB - This paper investigates the Bayesian process of identifying unknown model parameters given prior information and a set of noisy measurement data. There are two approaches being adopted in this research: one that uses the classical formula for measures and probability densities and one that leaves the underlying measure unchanged and updates the relevant random variable. The former is numerically tackled by a Markov chain Monte Carlo procedure based on the Metropolis- Hastings algorithm, whereas the latter is implemented via the ensemble/square root ensemble Kalman filters, as well as the functional approximation approaches in the form of the polynomial chaos based linear Bayesian filter and its corresponding square root algorithm. The study attempts to show the principal differences between full and linear Bayesian updates when a direct or a transformed version of measurements are taken into consideration. In this regard the comparison of both strategies is provided on the example of a steady state diffusion equation with nonlinear and transformed linear measurement operators.

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ER -

Comparison of numerical approaches to Bayesian updating

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Keywords

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