### Abstract

Here we use posterior densities based on relative entropy reference priors for two purposes. The first purpose is to identify data implicit in the use of informative priors. We represent an informative prior as the posterior from an experiment with a known likelihood and a reference prior. Minimizing the relative entropy distance between this posterior and the informative prior over choices of data results in a data set that can be regarded as representative of the information in the informative prior. The second implication from reference priors is obtained by replacing the informative prior with a class of densities from which one might wish to make inferences. For each density in this class, one can obtain a data set that minimizes a relative entropy. The maximum of these sample sizes as the inferential density varies over its class can be used as a guess as to how much data is required for the desired inferences. We bound this sample size above and below by other techniques that permit it to be approximated.

Original language | English (US) |
---|---|

Pages (from-to) | 173-184 |

Number of pages | 12 |

Journal | Journal of the American Statistical Association |

Volume | 91 |

Issue number | 433 |

DOIs | |

State | Published - Mar 1 1996 |

### Fingerprint

### Keywords

- Asymptotic normality
- Experimental design
- Information
- Relative entropy

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Implications of reference priors for prior information and for sample size.** / Clarke, Bertrand.

Research output: Contribution to journal › Article

*Journal of the American Statistical Association*, vol. 91, no. 433, pp. 173-184. https://doi.org/10.1080/01621459.1996.10476674

}

TY - JOUR

T1 - Implications of reference priors for prior information and for sample size

AU - Clarke, Bertrand

PY - 1996/3/1

Y1 - 1996/3/1

N2 - Here we use posterior densities based on relative entropy reference priors for two purposes. The first purpose is to identify data implicit in the use of informative priors. We represent an informative prior as the posterior from an experiment with a known likelihood and a reference prior. Minimizing the relative entropy distance between this posterior and the informative prior over choices of data results in a data set that can be regarded as representative of the information in the informative prior. The second implication from reference priors is obtained by replacing the informative prior with a class of densities from which one might wish to make inferences. For each density in this class, one can obtain a data set that minimizes a relative entropy. The maximum of these sample sizes as the inferential density varies over its class can be used as a guess as to how much data is required for the desired inferences. We bound this sample size above and below by other techniques that permit it to be approximated.

AB - Here we use posterior densities based on relative entropy reference priors for two purposes. The first purpose is to identify data implicit in the use of informative priors. We represent an informative prior as the posterior from an experiment with a known likelihood and a reference prior. Minimizing the relative entropy distance between this posterior and the informative prior over choices of data results in a data set that can be regarded as representative of the information in the informative prior. The second implication from reference priors is obtained by replacing the informative prior with a class of densities from which one might wish to make inferences. For each density in this class, one can obtain a data set that minimizes a relative entropy. The maximum of these sample sizes as the inferential density varies over its class can be used as a guess as to how much data is required for the desired inferences. We bound this sample size above and below by other techniques that permit it to be approximated.

KW - Asymptotic normality

KW - Experimental design

KW - Information

KW - Relative entropy

UR - http://www.scopus.com/inward/record.url?scp=0009064192&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009064192&partnerID=8YFLogxK

U2 - 10.1080/01621459.1996.10476674

DO - 10.1080/01621459.1996.10476674

M3 - Article

AN - SCOPUS:0009064192

VL - 91

SP - 173

EP - 184

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 433

ER -