A comparison of two Bayesian approaches for uncertainty quantification

Mara, Thierry A.; Delay, Frédérick; Lehmann, François; Younès, Anis

doi:10.1016/j.envsoft.2016.04.010

Cited by 15 publications

(13 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where The case d = 11 was studied in [21] in which the authors demonstrated that the MCPD draws were faster to generate than the MCMC draws (the case d = 25 was considered in [22]). Indeed, the MCPD sampler only required around one thousand evaluations of p(x|µ 1 , µ 2 , µ 3 , C) to obtain an accurate estimate of the variables' distributions.…”

Section: Numerical Exercisesmentioning

confidence: 99%

“…Let us now consider another challenging problem which was also analyzed in [21]. We target the twisted Gaussian density proposed in [13] and defined as follows, 2 1 + 10, 1) and p(x i ) = N (0, 1), ∀i = 3, .…”

Section: Ten-dimensional Twisted Gaussian Target Distributionmentioning

confidence: 99%

“…An overall of 54 560 model calls was necessary to assess the MCPDs, but thanks to the parallelization the actual waiting time (also called computational time unit) was about 6 500 model calls. Several comparisons between MCPD and a MCMC sampler have been carried out in [21] which demonstrated the efficiency of the MCPD approach.…”

mentioning

confidence: 99%

“…Of course, the selection of the optimization technique is a matter of choice. The algorithm used to compute the MCPDs is thoroughly explained in [22] and [21]. For convenience, it is succinctly recalled here.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Random Sampling from Joint Probability Distributions Defined in a Bayesian Framework

Mara¹,

Fahs²,

Shao³

et al. 2019

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

Random variables characterized by a joint probability distribution function (jpdf) defined in a Bayesian framework are generally sampled with Markov chain Monte Carlo (MCMC). The latter can be computationally demanding when the number of variables is high. As an alternative, the maximal conditional probability distribution (MCPD) sampler was recently introduced by some of the authors of the present article to readily and efficiently draw values randomly sampled from the desired jpdf. The MCPD approach provides the probability distribution of a given variable under the condition that the other variables maximized the conditional jpdf. However, contrarily to MCMC, MCPD does not provide enough draws to allow posterior uncertainty and sensitivity analyses of the computer model responses. In the present work, we show how to draw random samples from the MCPD draws under the requirement that the target jpdf possesses a particular dependence structure. Several numerical tests are carried out to prove the efficiency of the new sampling method. The new approach is used to perform the predictive uncertainty and sensitivity analyses of numerical models posterior to their statistical calibration from experimental data.

show abstract

Section: Numerical Exercisesmentioning

confidence: 99%

Section: Ten-dimensional Twisted Gaussian Target Distributionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Random Sampling from Joint Probability Distributions Defined in a Bayesian Framework

Mara¹,

Fahs²,

Shao³

et al. 2019

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Inoue et al [17] used electrical conductivity and matric pressure head measurements at different depths for the flow-transport inversion with the local search Levenberg-Marquardt algorithm. Recently, several Bayesian approaches, where measurements are combined with prior parameter information to provide posterior parameter distributions, have been investigated for the estimation of the unsaturated hydraulic soil parameters, among others [10,12,[18][19][20][21]. The term Bayesian is used to describe statistical inversion by considering [22]: (i) That model variables are random, (ii) that randomness describes the degree of information for their realization, and (iii) that the solution of the estimation problem is the posterior probability distribution from which several statistics can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment

Younès

Zaouali

Kanzari

et al. 2019

Water

Self Cite

View full text Add to dashboard Cite

Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this study, advanced experimental and numerical techniques are developed for an accurate estimation of the soil parameters. A laboratory unsaturated flow and solute transport experiment is conducted on a large undisturbed soil column of around 40 cm length. Bromide, used as a nonreactive contaminant, is injected at the surface of the undisturbed soil, followed by a leaching phase. The pressure measurements at different locations along the soil column as well as the outflow bromide concentration are collected during the experiment and used for the statistical calibration of flow and solute transport. The Richards equation, combined with constitutive relations for water content and permeability, is used to describe unsaturated flow. Both linear and non-equilibrium mobile–immobile transport models are investigated for the solute transport. All hydraulic and mass transport parameters are inferred using a one-step Bayesian estimation with the Markov chain Monte Carlo sampler. The results prove that the pressure and concentration measurements are able to identify almost all hydraulic and mass transport parameters. The mobile–immobile transport model better reproduces the infiltration experiment. It produces narrower uncertainty intervals for soil parameters and predictive output concentrations.

show abstract

Exploring the variance contributions of correlated model parameters: A sampling-based approach and its application in traffic simulation models

Ge¹,

Menéndez

2021

Applied Mathematical Modelling

View full text Add to dashboard Cite

A comparison of two Bayesian approaches for uncertainty quantification

Abstract: To cite this version:parameters are inferred. The results show that parameter and predictive uncertainties can be accurately assessed with both the MCMC and MCPD approaches.

Cited by 15 publications

References 33 publications

Random Sampling from Joint Probability Distributions Defined in a Bayesian Framework

Random Sampling from Joint Probability Distributions Defined in a Bayesian Framework

Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment

Exploring the variance contributions of correlated model parameters: A sampling-based approach and its application in traffic simulation models

Contact Info

Product

Resources

About