  We introduce a novel approach called the Bayesian Jackknife empirical
likelihood method for analyzing survey data obtained from various unequal
probability sampling designs. This method is particularly applicable to
parameters described by U-statistics. Theoretical proofs establish that under a
non-informative prior, the Bayesian Jackknife pseudo-empirical likelihood ratio
statistic converges asymptotically to a normal distribution. This statistic can
be effectively employed to construct confidence intervals for complex survey
samples. In this paper, we investigate various scenarios, including the
presence or absence of auxiliary information and the use of design weights or
calibration weights. We conduct numerical studies to assess the performance of
the Bayesian Jackknife pseudo-empirical likelihood ratio confidence intervals,
focusing on coverage probability and tail error rates. Our findings demonstrate
that the proposed methods outperform those based solely on the jackknife
pseudo-empirical likelihood, addressing its limitations.
