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 proceedingConference contributionAcademicpeer-review

5 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 languageEnglish
Title of host publicationComputational Methods for Solids and Fluids
Subtitle of host publicationMultiscale Analysis, Probability Aspects and Model Reduction
EditorsAdnan Ibrahimbegovic
Place of PublicationCham
PublisherSpringer
Pages427-461
Number of pages35
ISBN (Electronic)978-3-319-27996-1
ISBN (Print)978-3-319-27994-7
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes
Event2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015 - Sarajevo, Bosnia and Herzegovina
Duration: 10 Jun 201512 Jun 2015
Conference number: 2

Publication series

NameComputational Methods in Applied Sciences
PublisherSpringer
Volume41
ISSN (Print)1871-3033

Conference

Conference2nd International Conference on Multiscale Computational Methods for Solids and Fluids 2015
CountryBosnia and Herzegovina
CitySarajevo
Period10/06/1512/06/15

Keywords

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

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