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International Journal for Uncertainty Quantification

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.v2.i2.60
pages 161-172

RELATIONSHIP BETWEEN BAYESIAN AND FREQUENTIST SIGNIFICANCE INDICES

Marcio Diniz
Department of Statistics, Federal University of Sao Carlos, Rod. Washington Luis, km 235, Sao Carlos, SP, 13565-905, Brazil
Carlos A. B. Pereira
Mathematics and Statistics Institute, University of Sao Paulo, Sao Paulo, SP, Brazil
Adriano Polpo
Department of Statistics, Federal University of Sao Carlos, Rod. Washington Luis, km 235, Sao Carlos, SP, 13565-905, Brazil
Julio M. Stern
Mathematics and Statistics Institute, University of Sao Paulo, Sao Paulo, SP, Brazil
Sergio Wechsler
Mathematics and Statistics Institute, University of Sao Paulo, Sao Paulo, SP, Brazil

ABSTRACT

The goal of this paper is to illustrate how two significance indices−the frequentist p-value and Bayesian e-value− have a straight mathematical relationship. We calculate these indices for standard statistical situations in which sharp null hypotheses are being tested. The p-value considered here is based on the likelihood ratio statistic. The existence of a functional relationship between these indices could surprise readers because they are computed in different spaces: p-values in the sample space and e-values in the parameter space.