Bayesian Pseudo Empirical Likelihood Inference for Complex Surveys
Changbao Wu, University of Waterloo
Abstract: Bayesian inference for finite population problems faces major hurdles
in all three phases of the inferential procedure: the formulation of
a likelihood, the specification of a prior, and the validity of the
posterior inferences under the traditional design-based framework.
The empirical likelihood function can be used as the basis for
Bayesian inference and posterior intervals are valid for independent
and identically distributed observations (Lazar, 2003). However, this
is not the case for complex survey data, even if the design is simple
random sampling without replacement. We show that the pseudo empirical
likelihood, first proposed by Chen and Sitter (1999) and further refined
by Wu and Rao (2006), can be used for Bayesian inference under general
unequal probability sampling designs. With the non-informative
prior, Bayesian pseudo empirical likelihood intervals for the population
mean have asymptotically correct coverage probabilities under the design-based
framework. Two practically important cases are discussed: (i) the incorporation
of known auxiliary population information for the construction of Bayesian
intervals using the basic design weights; and (ii) the calculation of
Bayesian intervals using weights which have already been calibrated by
the known auxiliary information.
This is joint work with J.N.K. Rao of Carleton University.