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

Bayesian jackknife empirical likelihood with complex surveys