Experimental design represents the typical context in which the interplay between Bayesian and frequentist methodology is natural and useful. Before the data are observed, it is licit and unavoidable even for a Bayesian statistician to take into account sample variability for the evaluation of statistical procedures and for decision making. At the same time, design planning fatally involves a number of pre-experimental choices that even a frequentist statistician is forced to make, preferably by exploiting external sources of knowledge. In this paper we discuss this mutual exchange between Bayesian and frequentist methodology, with specific focus on the primary crucial aspect of experimental designs, that is sample size determination (SSD). We review this topic by highlighting how the interplay between two prior distributions helps in managing the close relationship between the two approaches. Although the distinction between decisional and performance-based methods for Bayesian SSD is discussed, the main interest of this article is on the latter.We propose a general framework that includes several performance-based methods as special cases and thus makes the comparison of their characteristics easier. Finally, we extend the overview to robust methods for Bayesian SSD that allow to deal with the critical issue of sensitivity to prior elicitation. Illustrative examples are provided for normal models. © Sapienza Universitá di Roma 2014.

Bayesian-frequentist sample size determination: A game of two priors / Brutti, Pierpaolo; DE SANTIS, Fulvio; Gubbiotti, Stefania. - In: METRON. - ISSN 0026-1424. - STAMPA. - 72:2(2014), pp. 133-151. [10.1007/s40300-014-0043-2]

Bayesian-frequentist sample size determination: A game of two priors

BRUTTI, Pierpaolo;DE SANTIS, Fulvio;GUBBIOTTI, STEFANIA
2014

Abstract

Experimental design represents the typical context in which the interplay between Bayesian and frequentist methodology is natural and useful. Before the data are observed, it is licit and unavoidable even for a Bayesian statistician to take into account sample variability for the evaluation of statistical procedures and for decision making. At the same time, design planning fatally involves a number of pre-experimental choices that even a frequentist statistician is forced to make, preferably by exploiting external sources of knowledge. In this paper we discuss this mutual exchange between Bayesian and frequentist methodology, with specific focus on the primary crucial aspect of experimental designs, that is sample size determination (SSD). We review this topic by highlighting how the interplay between two prior distributions helps in managing the close relationship between the two approaches. Although the distinction between decisional and performance-based methods for Bayesian SSD is discussed, the main interest of this article is on the latter.We propose a general framework that includes several performance-based methods as special cases and thus makes the comparison of their characteristics easier. Finally, we extend the overview to robust methods for Bayesian SSD that allow to deal with the critical issue of sensitivity to prior elicitation. Illustrative examples are provided for normal models. © Sapienza Universitá di Roma 2014.
2014
sample size; robust methods; experimental design; simulation-based approach; bayesian analysis; two priors; clinical trials
01 Pubblicazione su rivista::01a Articolo in rivista
Bayesian-frequentist sample size determination: A game of two priors / Brutti, Pierpaolo; DE SANTIS, Fulvio; Gubbiotti, Stefania. - In: METRON. - ISSN 0026-1424. - STAMPA. - 72:2(2014), pp. 133-151. [10.1007/s40300-014-0043-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/620989
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