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An exact non‐iterative sampling procedure for discrete missing data problems

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  • Guo‐Liang Tian
  • Ming Tan
  • Kai Wang Ng

Abstract

Many statistical problems can be formulated as discrete missing data problems (MDPs). Examples include change‐point problems, capture and recapture models, sample survey with non‐response, zero‐inflated Poisson models, medical screening/diagnostic tests and bioassay. This paper proposes an exact non‐iterative sampling algorithm to obtain independently and identically distributed (i.i.d.) samples from posterior distribution in discrete MDPs. The new algorithm is essentially a conditional sampling, thus completely avoiding problems of convergence and slow convergence in iterative algorithms such as Markov chain Monte Carlo. Different from the general inverse Bayes formulae (IBF) sampler of Tan, Tian and Ng (Statistica Sinica, 13, 2003, 625), the implementation of the new algorithm requires neither the expectation maximization nor the sampling importance resampling algorithms. The key idea is to first utilize the sampling‐wise IBF to derive the conditional distribution of the missing data given the observed data, and then to draw i.i.d. samples from the complete‐data posterior distribution. We first illustrate the method with a performing example and then apply the method to contingency tables with one supplemental margin for an human immunodeficiency virus study.

Suggested Citation

  • Guo‐Liang Tian & Ming Tan & Kai Wang Ng, 2007. "An exact non‐iterative sampling procedure for discrete missing data problems," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(2), pages 232-242, May.
  • Handle: RePEc:bla:stanee:v:61:y:2007:i:2:p:232-242
    DOI: 10.1111/j.1467-9574.2007.00345.x
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    Cited by:

    1. Nguyen, H.D. & Gouno, E., 2020. "Bayesian inference for Common cause failure rate based on causal inference with missing data," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    2. Wang, Wan-Lun & Fan, Tsai-Hung, 2012. "Bayesian analysis of multivariate t linear mixed models using a combination of IBF and Gibbs samplers," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 300-310.
    3. Liu, Yin & Tian, Guo-Liang, 2013. "A variant of the parallel model for sample surveys with sensitive characteristics," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 115-135.
    4. Guo-Liang Tian, 2014. "A new non-randomized response model: The parallel model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(4), pages 293-323, November.

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