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Bayesian Parameter Estimation via Filtering and Functional Approximations
TL;DR: In this paper, the inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed, and a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in computational model is given.
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Abstract: The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.
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Figures
![Figure 4: Conductivity field, from [36]](/figures/figure4-1-6jhsru5cnb6l.png)
Figure 4: Conductivity field, from [36] ![Figure 2: Time evolution of Lorenz-84 state and uncertainty with the LBU, from [33]](/figures/figure2-1-69wt9ymn630j.png)
Figure 2: Time evolution of Lorenz-84 state and uncertainty with the LBU, from [33] ![Figure 3: Diffusion domain, from [36]](/figures/figure3-1-85i7hwu4gxb3.png)
Figure 3: Diffusion domain, from [36] ![Figure 1: pdfs for linear Bayesian update, from [33]](/figures/figure1-1-400eelsz7nwx.png)
Figure 1: pdfs for linear Bayesian update, from [33] 
Figure 7: Perturbed observations of the cube of a RV, different updates — linear and quadratic update
![Figure 4: Conductivity field, from [36]](/figures/figure4-1-6jhsru5cnb6l.webp)
![Figure 2: Time evolution of Lorenz-84 state and uncertainty with the LBU, from [33]](/figures/figure2-1-69wt9ymn630j.webp)
![Figure 3: Diffusion domain, from [36]](/figures/figure3-1-85i7hwu4gxb3.webp)
![Figure 1: pdfs for linear Bayesian update, from [33]](/figures/figure1-1-400eelsz7nwx.webp)
Citations
•Journal Article
The theory that would not die
TL;DR: In the early 1730s Thomas Bayes (1701?-1761) was appointed minister at the Presbyterian Meeting House on Mount Sion, Tunbridge Wells, a town that had developed around the restorative chalybeate spring discovered there by Dudley, Lord North, in 1606 as discussed by the authors.
104
Comparison of Bayesian methods on parameter identification for a viscoplastic model with damage
Ehsan Adeli,Bojana Rosić,Hermann G. Matthies,Sven Reinstädler,Dieter Dinkler +4 more
- 01 Jul 2020
TL;DR: This study aims to observe which one of the mentioned methods is more suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, using a limited surface displacement measurement vector and see how much information is indeed needed to estimate the parameters accurately.
46
Reduced model of macro-scale stochastic plasticity identification by Bayesian inference: Application to quasi-brittle failure of concrete
TL;DR: In this paper, a probabilistic approach is proposed to bridge the gap between the macro-scale and meso-scale models by using a Voronoi-cell-based microstructure representation.
19
Application of Bayesian Networks for Estimation of Individual Psychological Characteristics
TL;DR: Bayesian networks are applied for developing more accurate overall estimations of psychological characteristics of an individual, based on psychological test results, which identify how much an individual possesses a certain trait.
5
A bayesian approach to model calibration and parameter estimation in potential drop measuring
Thomas Berg,Sven von Ende,Rolf Lammering +2 more
- 01 Jan 2017
TL;DR: The proposed Bayesian approach to determine the size of cracks in a structure indirectly via potential drop measurements in the presence of unknown material-dependent parameters bears the challenge of model calibration but of parameter estimation as well.
4
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Tamer Basar
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Monte Carlo Sampling Methods Using Markov Chains and Their Applications
TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates.
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Probability, random variables and stochastic processes
Athanasios Papoulis
- 01 Jan 1965
TL;DR: This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory.
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Probability, random variables, and stochastic processes
Athanasios Papoulis,S. Unnikrishna Pillai +1 more
- 01 Jan 2002
TL;DR: In this paper, the meaning of probability and random variables are discussed, as well as the axioms of probability, and the concept of a random variable and repeated trials are discussed.
12.7K
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