### Abstract

Bayesian analysis provides a consistent logical framework for processing data, inferring parameters and estimating relevant quantities in engineering prob- lems. However, its outcomes are valid conditional to the specific model assump- tions. Whether these assumptions are questioned, possibly because of some factors knowingly left out, they can be checked by further analysis of the available empirical data. Again, this can be done inside the Bayesian framework, by prob- abilistically comparing expanded models with the original one; however, this may be computational impractical in many applications. Test statistics and p-value analysis, historically developed under the frequentist approach but adapted to the Bayesian setting, provide an alternative for model checking coupled with proba- bilistic inference. In this chapter, we illustrate the relation between p-value analysis and Bayesian model comparison: after presenting it in a general context, we focus on Gaussian linear models under known perturbation, for which this relation can be stated in close formulas, and explore an example outside that domain.

Language | English |
---|---|

Title of host publication | Risk and Reliability Analysis |

Subtitle of host publication | Theory and Applications |

Place of Publication | Cham, Switzerland |

Publisher | Springer |

Pages | 317-339 |

Number of pages | 23 |

ISBN (Print) | 978-3-319-52424-5 |

DOIs | |

Publication status | Published - 25 Feb 2017 |

### Publication series

Name | Springer Series in Reliability Engineering |
---|---|

ISSN (Print) | 16147839 |

ISSN (Electronic) | 2196999X |

### Fingerprint

### Keywords

- Bayesian analysis
- model checking
- quality

### Cite this

*Risk and Reliability Analysis: Theory and Applications*(pp. 317-339). (Springer Series in Reliability Engineering). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-52425-2_14

}

*Risk and Reliability Analysis: Theory and Applications.*Springer Series in Reliability Engineering, Springer, Cham, Switzerland, pp. 317-339. https://doi.org/10.1007/978-3-319-52425-2_14

**Model checking after Bayesian inference.** / Pozzi, Matteo; Zonta, Daniele.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Model checking after Bayesian inference

AU - Pozzi, Matteo

AU - Zonta, Daniele

PY - 2017/2/25

Y1 - 2017/2/25

N2 - Bayesian analysis provides a consistent logical framework for processing data, inferring parameters and estimating relevant quantities in engineering prob- lems. However, its outcomes are valid conditional to the specific model assump- tions. Whether these assumptions are questioned, possibly because of some factors knowingly left out, they can be checked by further analysis of the available empirical data. Again, this can be done inside the Bayesian framework, by prob- abilistically comparing expanded models with the original one; however, this may be computational impractical in many applications. Test statistics and p-value analysis, historically developed under the frequentist approach but adapted to the Bayesian setting, provide an alternative for model checking coupled with proba- bilistic inference. In this chapter, we illustrate the relation between p-value analysis and Bayesian model comparison: after presenting it in a general context, we focus on Gaussian linear models under known perturbation, for which this relation can be stated in close formulas, and explore an example outside that domain.

AB - Bayesian analysis provides a consistent logical framework for processing data, inferring parameters and estimating relevant quantities in engineering prob- lems. However, its outcomes are valid conditional to the specific model assump- tions. Whether these assumptions are questioned, possibly because of some factors knowingly left out, they can be checked by further analysis of the available empirical data. Again, this can be done inside the Bayesian framework, by prob- abilistically comparing expanded models with the original one; however, this may be computational impractical in many applications. Test statistics and p-value analysis, historically developed under the frequentist approach but adapted to the Bayesian setting, provide an alternative for model checking coupled with proba- bilistic inference. In this chapter, we illustrate the relation between p-value analysis and Bayesian model comparison: after presenting it in a general context, we focus on Gaussian linear models under known perturbation, for which this relation can be stated in close formulas, and explore an example outside that domain.

KW - Bayesian analysis

KW - model checking

KW - quality

UR - http://www.scopus.com/inward/record.url?scp=85014068554&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-52425-2_14

DO - 10.1007/978-3-319-52425-2_14

M3 - Chapter

SN - 978-3-319-52424-5

T3 - Springer Series in Reliability Engineering

SP - 317

EP - 339

BT - Risk and Reliability Analysis

PB - Springer

CY - Cham, Switzerland

ER -