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On a Posterior Predictive Density Sample Size Criterion
Author(s) -
NICOLERIS THEODOROS,
WALKER STEPHEN G.
Publication year - 2006
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2006.00462.x
Subject(s) - mathematics , independent and identically distributed random variables , sample size determination , statistics , dirichlet distribution , parametric statistics , conditional probability distribution , combinatorics , sample (material) , mathematical analysis , random variable , chemistry , chromatography , boundary value problem
. Let Ω be a space of densities with respect to some σ ‐finite measure μ and let Π be a prior distribution having support Ω with respect to some suitable topology. Conditional on f , let X n = ( X 1 ,…, X n ) be an independent and identically distributed sample of size n from f . This paper introduces a Bayesian non‐parametric criterion for sample size determination which is based on the integrated squared distance between posterior predictive densities. An expression for the sample size is obtained when the prior is a Dirichlet mixture of normal densities.