Alternative Bayes factors: Sample size determination and discriminatory power assessment |
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Authors: | Fulvio De Santis |
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Affiliation: | (1) Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza”, Piazzale Aldo Moro, 5, 00185 Roma, Italy |
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Abstract: | Alternative Bayes factors are families of methods used for hypothesis testing and model selection when sensitivity to priors
is a concern and also when prior information is weak or lacking. This paper deals with two related problems that arise in
the practical use of these model choice criteria: sample size determination and evaluation of discriminatory power. We propose
a pre-experimental approach to cope with both these issues. Specifically, extending the evidential approach of Royall (J Am Stat Assoc 95(451):760–780, 2000) and following De Santis (J Stat Plan Inference 124(1):121–144,
2004), we propose a criterion for sample size choice based on the predictive probability of observing decisive and correct
evidence. The basic idea is to select the minimal sample size that guarantees a sufficiently high pre-experimental probability
that an alternative Bayes factor provides strong evidence in favor of the true hypothesis. It is also argued that a predictive
analysis is a natural approach to the measurement of discriminatory power of alternative Bayes factors. The necessity of measuring
discrimination ability depends on the fact that alternative Bayes factors are, in general, less sensitive to prior specifications
than ordinary Bayes factors and that this gain in robustness corresponds to a reduced discriminative power. Finally, implementation
of the predictive approach with improper priors is discussed and possible strategies are proposed.
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Keywords: | Bayes factors Default Bayes factors Discriminatory power Experimental design Fractional Bayes factors Intrinsic Bayes factors Sample size Statistical evidence |
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