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A simple approach to constructing quasi-Sudoku-based sliced space-filling designs

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Abstract

Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced orthogonal array-based space-filling designs are useful experimental designs in several contexts, including computer experiments with categorical in addition to quantitative inputs and cross-validation. Here, we provide a straightforward construction of doubly orthogonal quasi-Sudoku Latin squares which can be used to generate quasi-sliced orthogonal arrays and, in turn, sliced space-filling designs which achieve uniformity in one- and two-dimensional projections for the full design and uniformity in two-dimensional projections for each slice. These constructions are very practical to implement and yield a spectrum of design sizes and numbers of factors not currently broadly available.

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References

  • Ai, M., Jiang, B., Li, K. (2014). Construction of sliced space-filling designs based on balanced sliced orthogonal arrays. Statistica Sinica, 24, 1685–1702.

  • Colbourn, C. J., Dinitz, J. H. (2006). Handbook of combinatorial designs. New York: CRC Press.

  • Donovan, D., Burrage, K., Burrage, P., McCourt, T. A., Thompson, H. B., Yazici, E. S. (2015). Estimates of the coverage of parameter space by latin hypercube and orthogonal sampling: connections between populations of models and experimental designs. Preprint arXiv:1510.03502.

  • Haaland, B., Qian, P. Z. (2010). An approach to constructing nested space-filling designs for multi-fidelity computer experiments. Statistica Sinica, 20(3), 1063.

  • Hedayat, A. S., Sloane, N. J. A., Stufken, J. (2012). Orthogonal arrays: theory and applications. New York: Springer Science & Business Media.

  • Keedwell, A. D., Dénes, J. (2015). Latin squares and their applications. New York: Elsevier.

  • Li, K., Jiang, B., Ai, M. (2015). Sliced space-filling designs with different levels of two-dimensional uniformity. Journal of Statistical Planning and Inference, 157, 90–99.

  • Pedersen, R. M., Vis, T. L. (2009). Sets of mutually orthogonal sudoku latin squares. The College Mathematics Journal, 40(3), 174–181.

  • Qian, P. Z., Wu, C. J. (2009). Sliced space-filling designs. Biometrika, 96(4), 945–956.

  • Raghavarao, D. (1971). Constructions and combinatorial problems in design of experiments (Vol. 4). New York: Wiley.

    MATH  Google Scholar 

  • Tang, B. (1993). Orthogonal array-based latin hypercubes. Journal of the American statistical association, 88(424), 1392–1397.

    Article  MathSciNet  MATH  Google Scholar 

  • USA Today. (2013). Daily crossword. 19 September 2013.

  • Xu, X., Haaland, B., Qian, P. Z. (2011). Sudoku-based space-filling designs. Biometrika, 98(3), 711–720.

  • Zhang, Q., Qian, P. Z. (2013). Designs for crossvalidating approximation models. Biometrika, 100(4), 997–1004.

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Authors and Affiliations

  1. Department of Mathematics, University of Queensland, Brisbane St Lucia, QLD, 4072, Australia

    Diane Donovan

  2. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 755 Ferst Drive, NW, Atlanta, 30332, GA, USA

    Benjamin Haaland

  3. Centre for Quantitative Medicine, Duke-NUS Graduate Medical School, 8 College Road, Singapore, 169857, Singapore

    Benjamin Haaland

  4. Department of Statistics and Applied Probability, National University of Singapore, Singapore, 117546, Singapore

    David J. Nott

Authors
  1. Diane Donovan
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  2. Benjamin Haaland
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  3. David J. Nott
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Correspondence to Benjamin Haaland.

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Donovan, D., Haaland, B. & Nott, D.J. A simple approach to constructing quasi-Sudoku-based sliced space-filling designs. Ann Inst Stat Math 69, 865–878 (2017). https://doi.org/10.1007/s10463-016-0565-x

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  • DOI: https://doi.org/10.1007/s10463-016-0565-x

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