# Uncertainty analysis

## Abstract

An evaluation is made of the suitability of analytical and statistical sampling methods for making uncertainty analyses. The adjoint method is found to be well-suited for obtaining sensitivity coefficients for computer programs involving large numbers of equations and input parameters. For this purpose the Latin Hypercube Sampling method is found to be inferior to conventional experimental designs. The Latin hypercube method can be used to estimate output probability density functions, but requires supplementary rank transformations followed by stepwise regression to obtain uncertainty information on individual input parameters. A simple Cork and Bottle problem is used to illustrate the efficiency of the adjoint method relative to certain statistical sampling methods. For linear models of the form Ax=b it is shown that a complete adjoint sensitivity analysis can be made without formulating and solving the adjoint problem. This can be done either by using a special type of statistical sampling or by reformulating the primal problem and using suitable linear programming software.

- Authors:

- Publication Date:

- Research Org.:
- Battelle Memorial Inst., Columbus, OH (USA). Office of Nuclear Waste Isolation

- OSTI Identifier:
- 5196673

- Report Number(s):
- ONWI-380

ON: DE82020058; TRN: 82-018398

- DOE Contract Number:
- AC06-76RL01830

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE WASTES FROM NUCLEAR FACILITIES; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; RADIOACTIVE WASTE DISPOSAL; PERFORMANCE; STATISTICAL MODELS; SENSITIVITY ANALYSIS; DATA COVARIANCES; PROBABILITY; MANAGEMENT; MATHEMATICAL MODELS; WASTE DISPOSAL; WASTE MANAGEMENT; 052002* - Nuclear Fuels- Waste Disposal & Storage; 990200 - Mathematics & Computers

### Citation Formats

```
Thomas, R E.
```*Uncertainty analysis*. United States: N. p., 1982.
Web. doi:10.2172/5196673.

```
Thomas, R E.
```*Uncertainty analysis*. United States. https://doi.org/10.2172/5196673

```
Thomas, R E. Mon .
"Uncertainty analysis". United States. https://doi.org/10.2172/5196673. https://www.osti.gov/servlets/purl/5196673.
```

```
@article{osti_5196673,
```

title = {Uncertainty analysis},

author = {Thomas, R E},

abstractNote = {An evaluation is made of the suitability of analytical and statistical sampling methods for making uncertainty analyses. The adjoint method is found to be well-suited for obtaining sensitivity coefficients for computer programs involving large numbers of equations and input parameters. For this purpose the Latin Hypercube Sampling method is found to be inferior to conventional experimental designs. The Latin hypercube method can be used to estimate output probability density functions, but requires supplementary rank transformations followed by stepwise regression to obtain uncertainty information on individual input parameters. A simple Cork and Bottle problem is used to illustrate the efficiency of the adjoint method relative to certain statistical sampling methods. For linear models of the form Ax=b it is shown that a complete adjoint sensitivity analysis can be made without formulating and solving the adjoint problem. This can be done either by using a special type of statistical sampling or by reformulating the primal problem and using suitable linear programming software.},

doi = {10.2172/5196673},

url = {https://www.osti.gov/biblio/5196673},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1982},

month = {3}

}