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

Enrico Fabrizi, Parthasarathi Lahiri

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.


Keywords


Bayes factor;Hypothesis testing;Model selection; Pseudo-maximumlikelihood;Cluster sampling

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References


J. O. BERGER (2001). Objective Bayesian Methods for Model Selection: Introduction and Comparison. In P. LAHIRI (ed.), Model Selection, Institute of Mathematical Statistics, Lecture Notes - Monograph series, Vol. 38.

W. G. COCHRAN (1977). Sampling Techniques. JohnWiley & Sons, New York.

W. E. DEMING, F. F. STEPHEN (1941). On the interpretation of censuses as samples. Journal of the American Statistical Association, 36, pp. 45–49.

W. E. DEMING (1953). On the distinction between enumerative and analytic surveys. Journal of the American Statistical Association, 48, pp. 244–255.

B. EFRON, A. GOUS (2001). Scales of Evidence for Model Selection: Fisher versus Jeffreys. In P. LAHIRI (ed.), Model Selection, Institute ofMathematical Statistics, LectureNotes - Monograph series, Vol. 38.

B. I. GRAUBARD, E. L. KORN (2002). Inference for superpopulation parameters using sample surveys. Statistical Science, 17, pp. 73–96.

W. E. DEMING (1953). Maximum Likelihood Estimation for the Beta-Binomial Distribution and an Application to the Household Distribution of the Total Number of Cases of a Disease. Biometrics, 29, pp. 637–648.

M. H. HANSEN, W. G. MADOW, B. J. TEPPING (1983). An Evaluation of Model- Dependent and Probability-Sampling Inference in Sample Surveys. Journal of the American Statistical Association, 78, pp. 776–793.

D. HOLT, T. M. F. SMITH, P. D. WINTER (1980). Regression Analysis of Data from Complex Surveys. Journal of the Royal Statistical Society, Ser. A, 143, pp. 474–487.

D. HOLT (1989). Introduction to Part C. In C. J. SKINNER, D. HOLT, T. M. F. SMITH (eds.), Analysis of Complex Surveys, JohnWiley & Sons, Chicester, pp. 209–220.

C. T. ISAKI, W. A. FULLER (1982). Survey Design under the Regression Superpopulation Model. Journal of the American Statistical Association, 77, pp. 89–96.

H. JEFFREYS (1961). Theory of Probability. Oxford University Press, Oxford.

P. LAHIRI (2001). Model Selection. Institute of Mathematical Statistics, Lecture Notes - Monograph series, Vol. 38.

R. E. KASS, L.WASSERMANN (1995). A Reference Test for Nested Hypotheses and Its Relationship to the Schwartz Criterion. Journal of the American Statistical Association, 90, pp. 928–934.

P. S. KOTT (1989). Robust Small Domain Estimation using Random Effects Modelling. Survey Methodology, 15, pp. 3–12.

P. S. KOTT (1991). A Model-Based Look at Linear Regression with Survey Data. The American Statistician, 45, pp. 107–112.

D. PFEFFERMANN (2009). Inference under informative sampling. In D. PFEFFERMANN, C. R. RAO (eds.), Handbook of Statistics 29: Sample Surveys: Inference and Analysis, Elsevier, Amsterdam, pp. 455–487.

C. E. SÄRNDAL, B. SWENSSON, J.WRETMAN (1992). Model Assisted Survey Sampling. Springer-Verlag, New York.

S. R. SEARLE, G. CASELLA, C. E. MCCULLOGH (1996). Variance Components. John Wiley & Sons, New York.

G. SCHWARTZ (1978). Estimating the dimension of a model. The Annals of Statistics, 6, pp. 461–464.

C. J. SKINNER (1989). Introduction to Part A. In C. J. SKINNER, D. HOLT, T. M. F. SMITH (eds.), Analysis of Complex Surveys, JohnWiley & Sons, Chicester, pp. 23–28.

D. J. SPIEGELHALTER, N. G. BEST, B. P. CARLIN, A. VAN DER LINDE (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Ser. B, 64, pp. 583–639.




DOI: 10.6092/issn.1973-2201/4325