In this article we consider the sample size determination problem in the context of robust Bayesian parameter estimation of the Bernoulli model. Following a robust approach, we consider classes of conjugate Beta prior distributions for the unknown parameter. We assume that inference is robust if posterior quantities of interest (such as point estimates and limits of credible intervals) do not change too much as the prior varies in the selected classes of priors. For the sample size problem, we consider criteria based on predictive distributions of lower bound, upper bound and range of the posterior quantity of interest. The sample size is selected so that, before observing the data, one is confident to observe a small value for the posterior range and, depending on design goals, a large (small) value of the lower (upper) bound of the quantity of interest. We also discuss relationships with and comparison to non robust and non informative Bayesian methods.

Predictive control of posterior robustness for sample size choice in a Bernoulli model / DE SANTIS, Fulvio; Maria Clara, Fasciolo; Gubbiotti, Stefania. - In: STATISTICAL METHODS & APPLICATIONS. - ISSN 1618-2510. - STAMPA. - 22:3(2013), pp. 319-340. [10.1007/s10260-012-0225-0]

Predictive control of posterior robustness for sample size choice in a Bernoulli model

DE SANTIS, Fulvio;GUBBIOTTI, STEFANIA
2013

Abstract

In this article we consider the sample size determination problem in the context of robust Bayesian parameter estimation of the Bernoulli model. Following a robust approach, we consider classes of conjugate Beta prior distributions for the unknown parameter. We assume that inference is robust if posterior quantities of interest (such as point estimates and limits of credible intervals) do not change too much as the prior varies in the selected classes of priors. For the sample size problem, we consider criteria based on predictive distributions of lower bound, upper bound and range of the posterior quantity of interest. The sample size is selected so that, before observing the data, one is confident to observe a small value for the posterior range and, depending on design goals, a large (small) value of the lower (upper) bound of the quantity of interest. We also discuss relationships with and comparison to non robust and non informative Bayesian methods.
2013
conjugate analysis; bayesian robustness; sample size determination; clinical trials
01 Pubblicazione su rivista::01a Articolo in rivista
Predictive control of posterior robustness for sample size choice in a Bernoulli model / DE SANTIS, Fulvio; Maria Clara, Fasciolo; Gubbiotti, Stefania. - In: STATISTICAL METHODS & APPLICATIONS. - ISSN 1618-2510. - STAMPA. - 22:3(2013), pp. 319-340. [10.1007/s10260-012-0225-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/515475
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