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Nonparametric Bayesian testing for monotonicity

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  • J. G. Scott
  • T. S. Shively
  • S. G. Walker

Abstract

This paper adopts a nonparametric Bayesian approach to testing whether a function is monotone. Two new families of tests are constructed. The first uses constrained smoothing splines with a hierarchical stochastic-process prior that explicitly controls the prior probability of monotonicity. The second uses regression splines together with two proposals for the prior over the regression coefficients. Via simulation, the finite-sample performance of the tests is shown to improve upon existing frequentist and Bayesian methods. The asymptotic properties of the Bayes factor for comparing monotone versus nonmonotone regression functions in a Gaussian model are also studied. Our results significantly extend those currently available, which chiefly focus on determining the dimension of a parametric linear model.

Suggested Citation

  • J. G. Scott & T. S. Shively & S. G. Walker, 2015. "Nonparametric Bayesian testing for monotonicity," Biometrika, Biometrika Trust, vol. 102(3), pages 617-630.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:3:p:617-630.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv023
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    Cited by:

    1. C Rohrbeck & D A Costain & A Frigessi, 2018. "Bayesian spatial monotonic multiple regression," Biometrika, Biometrika Trust, vol. 105(3), pages 691-707.

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