×

zbMATH — the first resource for mathematics

Probabilistic sensitivity analysis of complex models: a Bayesian approach. (English) Zbl 1046.62027
Summary: In many areas of science and technology, mathematical models are built to simulate complex real world phenomena. Such models are typically implemented in large computer programs and are also very complex, such that the way that the model responds to changes in its inputs is not transparent. Sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs. This may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application.
A broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model’s output to variation in its inputs. In practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs, an approach which is known as probabilistic sensitivity analysis.
We present a Bayesian framework which unifies the various tools of probabilistic sensitivity analysis. The Bayesian approach is computationally highly efficient. It allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard Monte Carlo methods. Furthermore, all measures of interest may be computed from a single set of runs.

MSC:
62F15 Bayesian inference
62P99 Applications of statistics
65C05 Monte Carlo methods
93A30 Mathematical modelling of systems (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baker R. D., IMA J. Mangmnt Sci. 12 pp 1– (2001)
[2] Bayarri M., Proc. Wrkshp Foundations for Verification and Validation in the 21st Century (2002)
[3] Cox D. C., IEEE Trans. Reliab. 31 pp 265– (1982)
[4] DOI: 10.1198/016214501753168370 · Zbl 1017.62019 · doi:10.1198/016214501753168370
[5] Craig P. S., Case Studies in Bayesian Statistics pp 36– (1997)
[6] DOI: 10.1063/1.1680571 · doi:10.1063/1.1680571
[7] Currin C., J. Am. Statist. Ass. 86 pp 953– (1991)
[8] S. French (2003 ) Modelling, making inferences and making decisions: the roles of sensitivity analysis . , 11 , 229 -252 . · Zbl 1045.62004
[9] Haylock R. G., Bayesian Statistics 5 pp 629– (1996)
[10] Helton J. C., Sensitivity Analysis pp 101– (2000)
[11] DOI: 10.1016/0951-8320(96)00002-6 · doi:10.1016/0951-8320(96)00002-6
[12] DOI: 10.1111/1467-9868.00294 · Zbl 1007.62021 · doi:10.1111/1467-9868.00294
[13] Kleijnen J. P. C., J. Statist. Computn Simuln 57 pp 111– (1997)
[14] DOI: 10.1016/S0951-8320(98)00091-X · doi:10.1016/S0951-8320(98)00091-X
[15] DOI: 10.1061/(ASCE)0733-947X(1999)125:5(421) · doi:10.1061/(ASCE)0733-947X(1999)125:5(421)
[16] Neal R., Bayesian Statistics 6 pp 69– (1999)
[17] J. Oakley (2002 ) Value of information for complex cost-effectiveness models .Technical Report 533/02. Department of Probability and Statistics, University of Sheffield, Sheffield.
[18] DOI: 10.1111/1467-9884.00300 · doi:10.1111/1467-9884.00300
[19] DOI: 10.1093/biomet/89.4.769 · doi:10.1093/biomet/89.4.769
[20] DOI: 10.1016/0378-3758(91)90002-V · Zbl 0829.65024 · doi:10.1016/0378-3758(91)90002-V
[21] O’Hagan A., Bayesian Statistics 4 pp 345– (1992)
[22] O’Hagan A., Kendall’s Advanced Theory of Statistics (1994)
[23] O’Hagan A., Bayesian Statistics 6 pp 503– (1999)
[24] Sacks J., Statist. Sci. 4 pp 409– (1989)
[25] Saltelli A., Sensitivity Analysis (2000) · Zbl 0961.62091
[26] DOI: 10.1016/0951-8320(95)00099-2 · doi:10.1016/0951-8320(95)00099-2
[27] DOI: 10.1198/016214502388618447 · Zbl 1073.62602 · doi:10.1198/016214502388618447
[28] DOI: 10.1214/ss/1009213004 · doi:10.1214/ss/1009213004
[29] Saltelli A., Technometrics 41 pp 39– (1999)
[30] Sobol’ I. M., Math. Modlng Comput. Expt 1 pp 407– (1993)
[31] Welch W. J., Technometrics 34 pp 15– (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.