### A design-based approximation to the Bayes Information Criterion in finite population sampling

#### Abstract

In this article, various issues related to the implementation of the usual Bayesian Information Criterion (BIC) are critically examined in the context of modelling a finite population. A suitable design-based approximation to the BIC is proposed in order to avoid the derivation of the exact likelihood of the sample which is often very complex in a finite population sampling. The approximation is justified using a theoretical argument and a Monte Carlo simulation study.

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DOI: 10.6092/issn.1973-2201/4325