### Abstract

Original language | English |
---|---|

Pages (from-to) | 158-170 |

Journal | Journal of Mathematical Psychology |

Volume | 72 |

DOIs | |

Publication status | Published - 2016 |

### Fingerprint

### Cite this

}

**Automatic Bayes factors for testing variances of two independent normal distributions.** / Böing-Messing, F.; Mulder, J.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Automatic Bayes factors for testing variances of two independent normal distributions

AU - Böing-Messing, F.

AU - Mulder, J.

PY - 2016

Y1 - 2016

N2 - Researchers are frequently interested in testing variances of two independent populations. We often would like to know whether the population variances are equal, whether population 1 has smaller variance than population 2, or whether population 1 has larger variance than population 2. In this article we consider the Bayes factor, a Bayesian model selection and hypothesis testing criterion, for this multiple hypothesis test. Application of Bayes factors requires specification of prior distributions for the model parameters. Automatic Bayes factors circumvent the difficult task of prior elicitation by using data-driven mechanisms to specify priors in an automatic fashion. In this article we develop different automatic Bayes factors for testing two variances: first we apply the fractional Bayes factor (FBF) to the testing problem. It is shown that the FBF does not always function as Occam’s razor. Second we develop a new automatic balanced Bayes factor with equal priors for the variances. Third we propose a Bayes factor based on an adjustment of the marginal likelihood in the FBF approach. The latter two methods always function as Occam’s razor. Through theoretical considerations and numerical simulations it is shown that the third approach provides strongest evidence in favor of the true hypothesis.

AB - Researchers are frequently interested in testing variances of two independent populations. We often would like to know whether the population variances are equal, whether population 1 has smaller variance than population 2, or whether population 1 has larger variance than population 2. In this article we consider the Bayes factor, a Bayesian model selection and hypothesis testing criterion, for this multiple hypothesis test. Application of Bayes factors requires specification of prior distributions for the model parameters. Automatic Bayes factors circumvent the difficult task of prior elicitation by using data-driven mechanisms to specify priors in an automatic fashion. In this article we develop different automatic Bayes factors for testing two variances: first we apply the fractional Bayes factor (FBF) to the testing problem. It is shown that the FBF does not always function as Occam’s razor. Second we develop a new automatic balanced Bayes factor with equal priors for the variances. Third we propose a Bayes factor based on an adjustment of the marginal likelihood in the FBF approach. The latter two methods always function as Occam’s razor. Through theoretical considerations and numerical simulations it is shown that the third approach provides strongest evidence in favor of the true hypothesis.

U2 - 10.1016/j.jmp.2015.08.001

DO - 10.1016/j.jmp.2015.08.001

M3 - Article

VL - 72

SP - 158

EP - 170

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

SN - 0022-2496

ER -