## Abstract

Standard Bayesian inferences concerning a normal mean are considered when, for robustness reasons, Cauchy prior distributions are utilized. The inferences considered include testing a point null hypothesis, one-sided testing, estimation, and credible sets. A convenient way of presenting information for the statistical consumer is to give contour graphs of the Bayes factor, posterior mean, variance, etc., with respect to the prior parameters. This allows the readers to determine conclusions for their individual prior beliefs. The graphs also are useful for determination of sensitivity to the prior inputs. Using simple computational algorithms based on a mixture importance sampling algorithm, many of these contour graphs can be created extremely quickly.

Original language | English |
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Pages (from-to) | 381-399 |

Number of pages | 19 |

Journal | Computational Statistics and Data Analysis |

Volume | 33 |

Issue number | 4 |

DOIs | |

State | Published - 28 Jun 2000 |

## Keywords

- Bayes factor
- Credible sets
- Mixture importance sampling
- One-sided testing
- P -value
- Point null hypothesis
- Posterior mean
- Posterior variance
- Robust Bayesian analysis