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arXiv · 1304.3378

Nonparametric Bayesian testing for monotonicity

James G. Scott·Thomas S. Shively·Stephen G. Walker
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Abstract

This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together 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. The finite-sample performance of the tests is shown via simulation to improve upon existing frequentist and Bayesian methods. The asymptotic properties of the Bayes factor for comparing monotone versus non-monotone 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.

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James G. Scott, Thomas S. Shively, Stephen G. Walker. 2014-06-01. Nonparametric Bayesian testing for monotonicity. https://arxiv.org/abs/1304.3378

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