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# A note on the Bayesian analysis of experiments with correlated multiple responses using a matrix-logarithmic covariance model

## Abstract

In the literature, analysis of multiple responses from experiments with replicates has modeled the covariance matrix directly as linear models of the transformed variances and correlations, i.e., covariance modeling. This article considers models based on the matrix- logarithm of the covariance matrix. This so-called log-covariance modeling is illustrated with data from actual experiments and compared with the traditional covariance modeling.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Soochow Univ., Suzhou (China)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1558204

- Report Number(s):
- [LA-UR-18-27818]

[Journal ID: ISSN 0748-8017]

- Grant/Contract Number:
- [89233218CNA000001]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Quality and Reliability Engineering International

- Additional Journal Information:
- [Journal Name: Quality and Reliability Engineering International]; Journal ID: ISSN 0748-8017

- Publisher:
- Wiley

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Hamada, Michael S., Jaramillo, Brandon M., and Chiao, Chih‐Hua. A note on the Bayesian analysis of experiments with correlated multiple responses using a matrix-logarithmic covariance model. United States: N. p., 2019.
Web. doi:10.1002/qre.2540.
```

```
Hamada, Michael S., Jaramillo, Brandon M., & Chiao, Chih‐Hua. A note on the Bayesian analysis of experiments with correlated multiple responses using a matrix-logarithmic covariance model. United States. doi:10.1002/qre.2540.
```

```
Hamada, Michael S., Jaramillo, Brandon M., and Chiao, Chih‐Hua. Tue .
"A note on the Bayesian analysis of experiments with correlated multiple responses using a matrix-logarithmic covariance model". United States. doi:10.1002/qre.2540.
```

```
@article{osti_1558204,
```

title = {A note on the Bayesian analysis of experiments with correlated multiple responses using a matrix-logarithmic covariance model},

author = {Hamada, Michael S. and Jaramillo, Brandon M. and Chiao, Chih‐Hua},

abstractNote = {In the literature, analysis of multiple responses from experiments with replicates has modeled the covariance matrix directly as linear models of the transformed variances and correlations, i.e., covariance modeling. This article considers models based on the matrix- logarithm of the covariance matrix. This so-called log-covariance modeling is illustrated with data from actual experiments and compared with the traditional covariance modeling.},

doi = {10.1002/qre.2540},

journal = {Quality and Reliability Engineering International},

number = ,

volume = ,

place = {United States},

year = {2019},

month = {7}

}

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This content will become publicly available on July 23, 2020

Publisher's Version of Record

DOI: 10.1002/qre.2540

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Works referenced in this record:

##
Analyzing Experiments with Correlated Multiple Responses

journal, October 2001

- Chiao, Chih-Hua; Hamada, Michael
- Journal of Quality Technology, Vol. 33, Issue 4

##
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- Quality Engineering, Vol. 23, Issue 3

##
A Posterior Predictive Approach to Multiple Response Surface Optimization

journal, April 2004

- Peterson, John J.
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##
Planning and Analyzing Experiments with Models that Distinguish Between Replicates and Repeats: Distinguishing Between Replicates and Repeats

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- Hamada, Michael S.; Steiner, Stefan H.; MacKay, R. Jock
- Quality and Reliability Engineering International, Vol. 33, Issue 3

##
The Matrix-Logarithmic Covariance Model

journal, March 1996

- Chiu, Tom Y. M.; Leonard, Tom; Tsui, Kam-Wah
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