Data free inference with processed data products

Chowdhary, K.; Najm, H. N.

doi:10.1007/s11222-014-9484-y

Data free inference with processed data products

Journal Article · Sat Jul 12 00:00:00 EDT 2014 · Statistics and Computing

DOI:https://doi.org/10.1007/s11222-014-9484-y· OSTI ID:1095511

Chowdhary, K. ^[1]; Najm, H. N. ^[1]

Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Here, we consider the context of probabilistic inference of model parameters given error bars or confidence intervals on model output values, when the data is unavailable. We introduce a class of algorithms in a Bayesian framework, relying on maximum entropy arguments and approximate Bayesian computation methods, to generate consistent data with the given summary statistics. Once we obtain consistent data sets, we pool the respective posteriors, to arrive at a single, averaged density on the parameters. This approach allows us to perform accurate forward uncertainty propagation consistent with the reported statistics.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1095511

Report Number(s):: SAND--2013-8500J; PII: 9484

Journal Information:: Statistics and Computing, Journal Name: Statistics and Computing Journal Issue: 1-2 Vol. 26; ISSN 0960-3174

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (15)

Elements of Information Theory Cover, Thomas M.; Thomas, Joy A. https://doi.org/10.1002/047174882x	book	April 2005
Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised posterior distribution White, S. R.; Kypraios, T.; Preston, S. P. Statistics and Computing, Vol. 25, Issue 2 https://doi.org/10.1007/s11222-013-9432-2	journal	November 2013
Uncertainty quantification of reaction mechanisms accounting for correlations introduced by rate rules and fitted Arrhenius parameters Prager, Jens; Najm, Habib N.; Sargsyan, Khachik Combustion and Flame, Vol. 160, Issue 9 https://doi.org/10.1016/j.combustflame.2013.01.008	journal	September 2013
Data-free inference of the joint distribution of uncertain model parameters Berry, Robert D.; Najm, Habib N.; Debusschere, Bert J. Journal of Computational Physics, Vol. 231, Issue 5 https://doi.org/10.1016/j.jcp.2011.10.031	journal	March 2012
Convex Optimization Boyd, Stephen; Vandenberghe, Lieven https://doi.org/10.1017/cbo9780511804441	book	January 2004
How Measurements of Rate Coefficients at Low Temperature Increase the Predictivity of Photochemical Models of Titan’s Atmosphere ^† Hébrard, E.; Dobrijevic, M.; Pernot, P. The Journal of Physical Chemistry A, Vol. 113, Issue 42 https://doi.org/10.1021/jp905524e	journal	October 2009
Approximate Bayesian Computation in Population Genetics Beaumont, Mark A.; Zhang, Wenyang; Balding, David J. Genetics, Vol. 162, Issue 4 https://doi.org/10.1093/genetics/162.4.2025	journal	December 2002
Information Theory and Statistical Mechanics Jaynes, E. T. Physical Review, Vol. 106, Issue 4 https://doi.org/10.1103/physrev.106.620	journal	May 1957
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations Xiu, Dongbin; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 24, Issue 2 https://doi.org/10.1137/s1064827501387826	journal	January 2002
Characterization of Externally Bayesian Pooling Operators Genest, Christian; McConway, Kevin J.; Schervish, Mark J. The Annals of Statistics, Vol. 14, Issue 2 https://doi.org/10.1214/aos/1176349934	journal	June 1986
Entropic Inference Caticha, Ariel arXiv https://doi.org/10.48550/arxiv.1011.0723	text	January 2010
Elements of Information Theory Cover, Thomas M.; Thomas, Joy A. John Wiley & Sons, Inc. https://doi.org/10.1002/0471200611	book	January 1991
Convex Optimization Boyd, Stephen; Vandenberghe, Lieven https://doi.org/10.1017/CBO9780511804441	book	January 2004
Entropic Inference Caticha, Ariel; Mohammad-Djafari, Ali; Bercher, Jean-François AIP Conference Proceedings https://doi.org/10.1063/1.3573619	conference	January 2011
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations Xiu, Dongbin; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 24, Issue 2 https://doi.org/10.1137/S1064827501387826	journal	January 2002

Similar Records

Data-free inference of uncertain model parameters.

Conference · Tue Jun 01 00:00:00 EDT 2010 · OSTI ID:1020452

Data-free inference of the joint distribution of uncertain model parameters.

Conference · Sat May 01 00:00:00 EDT 2010 · OSTI ID:1013797

Inference of reaction rate parameters based on summary statistics from experiments

Journal Article · Fri Oct 14 20:00:00 EDT 2016 · Proceedings of the Combustion Institute · OSTI ID:1325156

Related Subjects

97 MATHEMATICS AND COMPUTING
Bayesian inference
Markov Chain Monte Carlo
approximate Bayesian computation
maximum entropy
missing information
uncertainty quantification

Data free inference with processed data products

Citation Formats

References (15)

Similar Records

Related Subjects