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U-type and factorial designs for nonparametric Bayesian regression

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  • Yue, Rong-Xian
  • Wu, Jing-Wen

Abstract

This paper deals with the design problem for recovering a response surface by using a nonparametric Bayesian approach. The criterion for selecting the designs is based on the asymptotic average estimation variance, and three priors for the response are specified. We found the optimal design that minimizes the criterion over the lattice designs with s q-level factors and N runs. The approach we used is similar to that in Ma et al. (J. Statist. Plann. Inference 113 (2003) 323). We also obtained alternative expressions and lower bounds for the criterion corresponding to each of the three Bayes models for the two-level U-type design by using the column balance and row distance proposed in Fang et al. (J. Complexity 19 (2003) 692). These results mat be used to construct the two-level U-type designs for the nonparametric Bayesian models.

Suggested Citation

  • Yue, Rong-Xian & Wu, Jing-Wen, 2004. "U-type and factorial designs for nonparametric Bayesian regression," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 343-356, September.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:3:p:343-356
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    References listed on IDEAS

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    1. Yue, Rong-Xian, 2001. "A comparison of random and quasirandom points for nonparametric response surface design," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 129-142, June.
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    Cited by:

    1. Rong-Xian Yue & Xiao-Dong Zhou, 2010. "Bayesian robust designs for linear models with possible bias and correlated errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(1), pages 1-15, January.
    2. Rong-Xian Yue & Kashinath Chatterjee, 2010. "Bayesian U-type design for nonparametric response surface prediction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 219-231, September.

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