We consider the standard one-way ANOVA model; it is well-known that classical statistical procedures are based on a scalar non-centrality parameter. In this paper we explore both marginal likelihood and integrated likelihood functions for this parameter and we show that they exactly lead to the same answer. On the other hand, we prove that a fully Bayesian testing procedure may provide different conclusions, depending on what is considered to be the real quantity of interest in the model or, said differently, which are the competing hypotheses. We illustrate these issues via a real data example. © 2007 The Institute of Statistical Mathematics.
Some remarks on Bayesian inference for one-way ANOVA models / Fabrizio, Solari; Liseo, Brunero; Dongchu, Sun. - In: ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS. - ISSN 0020-3157. - STAMPA. - 60:3(2008), pp. 483-498. [10.1007/s10463-007-0117-5]
Some remarks on Bayesian inference for one-way ANOVA models
LISEO, Brunero;
2008
Abstract
We consider the standard one-way ANOVA model; it is well-known that classical statistical procedures are based on a scalar non-centrality parameter. In this paper we explore both marginal likelihood and integrated likelihood functions for this parameter and we show that they exactly lead to the same answer. On the other hand, we prove that a fully Bayesian testing procedure may provide different conclusions, depending on what is considered to be the real quantity of interest in the model or, said differently, which are the competing hypotheses. We illustrate these issues via a real data example. © 2007 The Institute of Statistical Mathematics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
