# The estimation of parameters in nonlinear, implicit measurement error models with experiment-wide measurements

## Abstract

Measurement error modeling is a statistical approach to the estimation of unknown model parameters which takes into account the measurement errors in all of the data. Approaches which ignore the measurement errors in so-called independent variables may yield inferior estimates of unknown model parameters. At the same time, experiment-wide variables (such as physical constants) are often treated as known without error, when in fact they were produced from prior experiments. Realistic assessments of the associated uncertainties in the experiment-wide variables can be utilized to improve the estimation of unknown model parameters. A maximum likelihood approach to incorporate measurements of experiment-wide variables and their associated uncertainties is presented here. An iterative algorithm is presented which yields estimates of unknown model parameters and their estimated covariance matrix. Further, the algorithm can be used to assess the sensitivity of the estimates and their estimated covariance matrix to the given experiment-wide variables and their associated uncertainties.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest Lab., Richland, WA (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 10156430

- Report Number(s):
- PNL-9794

ON: DE94012759

- DOE Contract Number:
- AC06-76RL01830

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: May 1994

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL PROTECTION; PARAMETRIC ANALYSIS; MATHEMATICAL MODELS; ARMS CONTROL; VERIFICATION; ERRORS; STATISTICS; ALGORITHMS; DATA COVARIANCES; MAXIMUM-LIKELIHOOD FIT; 990200; 350300; MATHEMATICS AND COMPUTERS

### Citation Formats

```
Anderson, K.K.
```*The estimation of parameters in nonlinear, implicit measurement error models with experiment-wide measurements*. United States: N. p., 1994.
Web. doi:10.2172/10156430.

```
Anderson, K.K.
```*The estimation of parameters in nonlinear, implicit measurement error models with experiment-wide measurements*. United States. doi:10.2172/10156430.

```
Anderson, K.K. Sun .
"The estimation of parameters in nonlinear, implicit measurement error models with experiment-wide measurements". United States.
doi:10.2172/10156430. https://www.osti.gov/servlets/purl/10156430.
```

```
@article{osti_10156430,
```

title = {The estimation of parameters in nonlinear, implicit measurement error models with experiment-wide measurements},

author = {Anderson, K.K.},

abstractNote = {Measurement error modeling is a statistical approach to the estimation of unknown model parameters which takes into account the measurement errors in all of the data. Approaches which ignore the measurement errors in so-called independent variables may yield inferior estimates of unknown model parameters. At the same time, experiment-wide variables (such as physical constants) are often treated as known without error, when in fact they were produced from prior experiments. Realistic assessments of the associated uncertainties in the experiment-wide variables can be utilized to improve the estimation of unknown model parameters. A maximum likelihood approach to incorporate measurements of experiment-wide variables and their associated uncertainties is presented here. An iterative algorithm is presented which yields estimates of unknown model parameters and their estimated covariance matrix. Further, the algorithm can be used to assess the sensitivity of the estimates and their estimated covariance matrix to the given experiment-wide variables and their associated uncertainties.},

doi = {10.2172/10156430},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun May 01 00:00:00 EDT 1994},

month = {Sun May 01 00:00:00 EDT 1994}

}