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A peeling algorithm for multiple testing on a random field

Author

Listed:
  • Joungyoun Kim

    (Chungbuk National University)

  • Donghyeon Yu

    (Inha University)

  • Johan Lim

    (Seoul National University)

  • Joong-Ho Won

    (Seoul National University)

Abstract

The optimal decision rule for testing hypothesis using observations or statistics on a two-dimensional lattice system is theoretically well-understood since Sun and Cai (J R Stat Soc Ser B (Stat Methodol) 71(2):393–424, 2009). However, its practical use still faces several difficulties that include the computation of the local index of significance (LIS). In this paper, we propose a peeling algorithm to compute the LIS, or equivalently the marginal posterior probability for the indicator of the true hypothesis for each site. We show that the proposed peeling algorithm has several advantages over the popular Markov chain Monte Carlo methods through an extensive numerical study. An application of the peeling algorithm to finding active voxels in a task-based fMRI experiment is also presented.

Suggested Citation

  • Joungyoun Kim & Donghyeon Yu & Johan Lim & Joong-Ho Won, 2018. "A peeling algorithm for multiple testing on a random field," Computational Statistics, Springer, vol. 33(1), pages 503-525, March.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0724-4
    DOI: 10.1007/s00180-017-0724-4
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    References listed on IDEAS

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    1. Sun, Wenguang & Cai, T. Tony, 2007. "Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 901-912, September.
    2. Hongyuan Cao & Wenguang Sun & Michael R. Kosorok, 2013. "The optimal power puzzle: scrutiny of the monotone likelihood ratio assumption in multiple testing," Biometrika, Biometrika Trust, vol. 100(2), pages 495-502.
    3. Hai Shu & Bin Nan & Robert Koeppe, 2015. "Multiple testing for neuroimaging via hidden Markov random field," Biometrics, The International Biometric Society, vol. 71(3), pages 741-750, September.
    4. Won, Joong-Ho & Lim, Johan & Yu, Donghyeon & Kim, Byung Soo & Kim, Kyunga, 2014. "Monotone false discovery rate," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 86-93.
    5. Wenguang Sun & T. Tony Cai, 2009. "Large‐scale multiple testing under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 393-424, April.
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