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Approximate Bayesian inference under informative sampling

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  • Z Wang
  • J K Kim
  • S Yang

Abstract

Summary Statistical inference with complex survey data is challenging because the sampling design can be informative, and ignoring it can produce misleading results. Current methods of Bayesian inference under complex sampling assume that the sampling design is noninformative for the specified model. In this paper, we propose a Bayesian approach which uses the sampling distribution of a summary statistic to derive the posterior distribution of the parameters of interest. Asymptotic properties of the method are investigated. It is directly applicable to combining information from two independent surveys and to calibration estimation in survey sampling. A simulation study confirms that it can provide valid estimation under informative sampling. We apply it to a measurement error problem using data from the Korean Longitudinal Study of Aging.

Suggested Citation

  • Z Wang & J K Kim & S Yang, 2018. "Approximate Bayesian inference under informative sampling," Biometrika, Biometrika Trust, vol. 105(1), pages 91-102.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:1:p:91-102.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx073
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    Cited by:

    1. Kristin McCullough & Tatiana Dmitrieva & Nader Ebrahimi, 2022. "New approximate Bayesian computation algorithm for censored data," Computational Statistics, Springer, vol. 37(3), pages 1369-1397, July.
    2. Gyuhyeong Goh & Jae Kwang Kim, 2021. "Accounting for model uncertainty in multiple imputation under complex sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 930-949, September.

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