The Effective Sample Size

Model selection procedures often depend explicitly on the sample size n of the experiment. One example is the Bayesian information criterion (BIC) criterion and another is the use of Zellner.Siow priors in Bayesian model selection. Sample size is well-defined if one has i.i.d real observations, but is not well-defined for vector observations or in non-i.i.d. settings; extensions of critera such as BIC to such settings thus requires a definition of effective sample size that applies also in such cases. A definition of effective sample size that applies to fairly general linear models is proposed and illustrated in a variety of situations. The definition is also used to propose a suitable .scale. for default proper priors for Bayesian model selection.