Published 6 issues per year
ISSN Print: 2152-5080
ISSN Online: 2152-5099
Indexed in
BAYESIAN INFERENCE FOR INVERSE PROBLEMS OCCURRING IN UNCERTAINTY ANALYSIS
ABSTRACT
The inverse problem considered here is the estimation of the distribution of a nonobserved random variable X, linked through a time-consuming physical model H to some noisy observed data Y. Bayesian inference is considered to account for prior expert knowledge on X in a small sample size setting. A Metropolis-Hastings-within-Gibbs algorithm is used to compute the posterior distribution of the parameters of the distribution of X through a data augmentation process. Since running H is quite expensive, this inference is achieved by a kriging emulator interpolating H from a numerical design of experiments (DOE). This approach involves several errors of different natures and, in this article, we pay effort to measure and reduce the possible impact of those errors. In particular, we propose to use the so-called DAC criterion to assess in the same exercise the relevance of the DOE and the prior distribution. After describing the calculation of this criterion for the emulator at hand, its behavior is illustrated on numerical experiments.
-
Fu Shuai, Hierarchical Bayesian LASSO for a negative binomial regression, Journal of Statistical Computation and Simulation, 86, 11, 2016. Crossref
-
Barbillon Pierre, Barthélémy Célia, Samson Adeline, Parameter estimation of complex mixed models based on meta-model approach, Statistics and Computing, 27, 4, 2017. Crossref
-
Veen Duco, Stoel Diederick, Schalken Naomi, Mulder Kees, van de Schoot Rens, Using the Data Agreement Criterion to Rank Experts’ Beliefs, Entropy, 20, 8, 2018. Crossref
-
Damblin Guillaume, Gaillard Pierre, Bayesian inference and non-linear extensions of the CIRCE method for quantifying the uncertainty of closure relationships integrated into thermal-hydraulic system codes, Nuclear Engineering and Design, 359, 2020. Crossref
-
Aryuyuen Sirinapa, Bayesian inference for the negative binomial-generalized Lindley regression model: properties and applications, Communications in Statistics - Theory and Methods, 2021. Crossref
-
Garoli Gabriel Y., Pilotto Rafael, Nordmann Rainer, de Castro Helio F., Identification of active magnetic bearing parameters in a rotor machine using Bayesian inference with generalized polynomial chaos expansion, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 12, 2021. Crossref
-
Bethencourt Loic, Dabachine Walid, Dejouy Vincent, Lalmiche Zakaria, Neuberger Karl, Ibnouhsein Issam, Chereau Sandrine, Mathelin Carole, Savy Nicolas, Pierre Philippe Saint, Bousquet Nicolas, Guiding Measurement Protocols of Connected Medical Devices Using Digital Twins: A Statistical Methodology Applied to Detecting and Monitoring Lymphedema, IEEE Access, 9, 2021. Crossref
-
Nagel Joseph B., Sudret Bruno, Hamiltonian Monte Carlo and Borrowing Strength in Hierarchical Inverse Problems, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 2, 3, 2016. Crossref