Nonparametric Bayesian testing for monotonicity
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.
Cite
@article{arxiv.1304.3378,
title = {Nonparametric Bayesian testing for monotonicity},
author = {James G. Scott and Thomas S. Shively and Stephen G. Walker},
journal= {arXiv preprint arXiv:1304.3378},
year = {2014}
}