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Hybrid schemes for exact conditional inference in discrete exponential families

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Abstract

Exact conditional goodness-of-fit tests for discrete exponential family models can be conducted via Monte Carlo estimation of p values by sampling from the conditional distribution of multiway contingency tables. The two most popular methods for such sampling are Markov chain Monte Carlo (MCMC) and sequential importance sampling (SIS). In this work we consider various ways to hybridize the two schemes and propose one standout strategy as a good general purpose method for conducting inference. The proposed method runs many parallel chains initialized at SIS samples across the fiber. When a Markov basis is unavailable, the proposed scheme uses a lattice basis with intermittent SIS proposals to guarantee irreducibility and asymptotic unbiasedness. The scheme alleviates many of the challenges faced by the MCMC and SIS schemes individually while largely retaining their strengths. It also provides diagnostics that guide and lend credibility to the procedure. Simulations demonstrate the viability of the approach.

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Notes

  1. This is the corrected value from that article, which is generally known to have been a typographical error.

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Acknowledgements

D. K. and R. Y. are supported by the National Science Foundation under Grant Nos. 1622449 and 1622369, respectively. The authors would like to thank an anonymous referee for suggesting that the validity of the scheme should be considered through the lens of unbiasedness.

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Authors and Affiliations

  1. Department of Statistical Science, Baylor University, One Bear Place #97140, Waco, TX, 76798, USA

    David Kahle

  2. Department of Operations Research, Naval Postgraduate School, 1411 Cunningham Road, Monterey, CA, 93943, USA

    Ruriko Yoshida

  3. Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX, 77341, USA

    Luis Garcia-Puente

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  1. David Kahle
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  2. Ruriko Yoshida
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  3. Luis Garcia-Puente
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Correspondence to David Kahle.

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Kahle, D., Yoshida, R. & Garcia-Puente, L. Hybrid schemes for exact conditional inference in discrete exponential families. Ann Inst Stat Math 70, 983–1011 (2018). https://doi.org/10.1007/s10463-017-0615-z

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  • DOI: https://doi.org/10.1007/s10463-017-0615-z

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