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J. G. Scott, T. S. Shively, S. G. Walker, Nonparametric Bayesian testing for monotonicity, Biometrika, Volume 102, Issue 3, September 2015, Pages 617–630, https://doi.org/10.1093/biomet/asv023
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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.