# Data free inference with processed data products

## Abstract

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.

- Authors:

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

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)

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

- OSTI Identifier:
- 1095511

- Report Number(s):
- SAND-2013-8500J

Journal ID: ISSN 0960-3174; PII: 9484

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Statistics and Computing

- Additional Journal Information:
- Journal Volume: 26; Journal Issue: 1-2; Journal ID: ISSN 0960-3174

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Chowdhary, K., and Najm, H. N.
```*Data free inference with processed data products*. United States: N. p., 2014.
Web. doi:10.1007/s11222-014-9484-y.

```
Chowdhary, K., & Najm, H. N.
```*Data free inference with processed data products*. United States. doi:10.1007/s11222-014-9484-y.

```
Chowdhary, K., and Najm, H. N. Sat .
"Data free inference with processed data products". United States.
doi:10.1007/s11222-014-9484-y. https://www.osti.gov/servlets/purl/1095511.
```

```
@article{osti_1095511,
```

title = {Data free inference with processed data products},

author = {Chowdhary, K. and Najm, H. N.},

abstractNote = {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.},

doi = {10.1007/s11222-014-9484-y},

journal = {Statistics and Computing},

number = 1-2,

volume = 26,

place = {United States},

year = {Sat Jul 12 00:00:00 EDT 2014},

month = {Sat Jul 12 00:00:00 EDT 2014}

}

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Cited by: 2works

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