Bayesian Error Propagation
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Request full-text Bayesian Error Propagation for a Kinetic Model of n-Propylbenzene Oxidation in a Shock TubeArticle in International Journal of Chemical Kinetics 46(7) · July 2014 with 40 ReadsDOI: 10.1002/kin.20855 1st Sebastian Mosbach2nd Je Hyeong asymmetric error Hong2.74 · University of Cambridge+ 23rd George Brownbridge19.72 · University of CambridgeLast asymmetric error propagation K. Brezinsky34.87 · University of Illinois at ChicagoShow more authorsAbstractWe apply a Bayesian parameter estimation technique to a chemical error propagation asymmetric error bars kinetic mechanism for n-propylbenzene oxidation in a shock tube to propagate errors in experimental data to errors in Arrhenius parameters and predicted species concentrations. We find that, to apply the methodology combining asymmetric errors successfully, conventional optimization is required as a preliminary step. This is carried out in two stages: First, a quasi-random global search using a Sobol low-discrepancy sequence is conducted, followed by a local optimization by means of a hybrid gradient-descent/Newton iteration method. The concentrations of 37 species at a variety of temperatures, pressures, and equivalence ratios are optimized against a total of 2378 experimental
Asymmetric Standard Deviation
observations. We then apply the Bayesian methodology to study the influence of uncertainties in the experimental measurements on some of the Arrhenius parameters in the model as well as some of the predicted species concentrations. Markov chain Monte Carlo algorithms are employed to sample from the posterior probability densities, making use of polynomial surrogates of higher order fitted to the model responses. We conclude that the methodology provides a useful tool for the analysis of distributions of model parameters and responses, in particular their uncertainties and correlations. Limitations of the method are discussed. For example, we find that using second-order response surfaces and assuming normal distributions for propagated errors is largely adequate, but not always.Do you want to read the rest of this article?Request full-text CitationsCitations12ReferencesReferences73Uncertainty and Sensitivity Analysis in Complex Plasma Chemistry Models"This philosophy has apparently informed the development of chemistry models in the low-temperature plasma physics community for the last few decades, which have seen the complexity of models steadily increasing. However, other communities facing similar difficulties, such as combustion science, have tended towards a different approach [51, 41, 44, 23, 35]. They favour
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Gaussian Error Propagation
Rheology » View All Publishers Publications Topics Collections | Librarians Authors My Cart propagation of error division Home > Publishers > AIP Publishing > The Journal of Chemical Physics > Volume 137 Number 14 > Article No data available. Please log in to see this content. You have no subscription access to this content. No metrics data to plot. The attempt to load metrics for this article https://www.researchgate.net/publication/261770207_Bayesian_Error_Propagation_for_a_Kinetic_Model_of_n-Propylbenzene_Oxidation_in_a_Shock_Tube has failed. The attempt to plot a graph for these metrics has failed. The full text of this article is not currently available. Bayesian uncertainty quantification and propagation in molecular dynamics simulations: A high performance computing framework Panagiotis Angelikopoulos1,a), Costas Papadimitriou2,b)and Petros Koumoutsakos1,c) Scitation Author Page PubMed Google Scholar View Affiliations Hide Affiliations Affiliations: 1 Computational Science and Engineering Laboratory, ETH Zürich, CH-8092 http://scitation.aip.org/content/aip/journal/jcp/137/14/10.1063/1.4757266 Zurich, Switzerland 2 Department of Mechanical Engineering, University of Thessaly, Pedion Areos, GR-38334 Volos, Greece a) Electronic mail: panagiotis.angelikopoulos@mavt.ethz.ch. b) Electronic mail: costasp@uth.gr. c) Electronic mail: petros@ethz.ch. J. Chem. Phys. 137, 144103 (Sun Oct 14 00:00:00 UTC 2012); http://dx.doi.org/10.1063/1.4757266 USD Buy: USD30.00 Rent: Rent this article for 10.1063/1.4757266 Previous Article Table of Contents Next Article Abstract Full Text References (79) Cited By (43) Data & Media Metrics Related Abstract We present a Bayesian probabilistic framework for quantifying and propagating the uncertainties in the parameters of force fields employed in molecular dynamics (MD) simulations. We propose a highly parallel implementation of the transitional Markov chain Monte Carlo for populating the posterior probability distribution of the MD force-field parameters. Efficient scheduling algorithms are proposed to handle the MD model runs and to distribute the computations in clusters with heterogeneous architectures. Furthermore, adaptive surrogate models are proposed in order to reduce the computational cost associated with the large number of MD model runs. The effectiveness and computational efficiency of the proposed Bayesian framework is demonstrated in MD simulations of liquid and gaseous argon.
© 2012 American Institute of Physics DOI: htapplications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example https://en.wikipedia.org/wiki/Uncertainty_quantification would be to predict the acceleration of a human body in a head-on crash with another car: even if we exactly knew the speed, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc., will lead to different results that can only be predicted in error propagation a statistical sense. Many problems in the natural sciences and engineering are also rife with sources of uncertainty. Computer experiments on computer simulations are the most common approach to study problems in uncertainty quantification.[1][2][3] Contents 1 Sources of uncertainty 1.1 Aleatoric and epistemic uncertainty 2 Two types of uncertainty quantification problems 2.1 bayesian error propagation Forward uncertainty propagation 2.2 Inverse uncertainty quantification 2.2.1 Bias correction only 2.2.2 Parameter calibration only 2.2.3 Bias correction and parameter calibration 3 Selective methodologies for uncertainty quantification 3.1 Methodologies for forward uncertainty propagation 3.2 Methodologies for inverse uncertainty quantification 3.2.1 Frequentist 3.2.2 Bayesian 3.2.2.1 Modular Bayesian approach 3.2.2.2 Fully Bayesian approach 4 Known issues 5 See also 6 References 7 Further reading Sources of uncertainty[edit] Uncertainty can enter mathematical models and experimental measurements in various contexts. One way to categorize the sources of uncertainty is to consider:[4] Parameter uncertainty, which comes from the model parameters that are inputs to the computer model (mathematical model) but whose exact values are unknown to experimentalists and cannot be controlled in physical experiments, or whose values cannot be exactly inferred by statistical methods. Examples are the local free-fall acceleration in a falling object experiment, various material properties in a finite element analysis for engineering, and multiplier