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Conditional inferential models: combining information for prior-free probabilistic inference

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  • Ryan Martin
  • Chuanhai Liu

Abstract

type="main" xml:id="rssb12070-abs-0001"> The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher dimension than the parameter. Here we show that features of the auxiliary variable are often fully observed and, in such cases, a simultaneous dimension reduction and information aggregation can be achieved by conditioning. This proposed conditioning strategy leads to efficient IM inference and casts new light on Fisher's notions of sufficiency, conditioning and also Bayesian inference. A differential-equation-driven selection of a conditional association is developed, and validity of the conditional IM is proved under some conditions. For problems that do not admit a conditional IM of the standard form, we propose a more flexible class of conditional IMs based on localization. Examples of local conditional IMs in a bivariate normal model and a normal variance components model are also given.

Suggested Citation

  • Ryan Martin & Chuanhai Liu, 2015. "Conditional inferential models: combining information for prior-free probabilistic inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 195-217, January.
  • Handle: RePEc:bla:jorssb:v:77:y:2015:i:1:p:195-217
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.77.issue-1
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    Cited by:

    1. Jin, Hua & Li, Song & Jin, Yaolan, 2016. "The IM-based method for testing the non-inferiority of odds ratio in matched-pairs design," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 145-151.
    2. Wu, Suofei & Hannig, Jan & Lee, Thomas C.M., 2022. "Uncertainty quantification for honest regression trees," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).

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