%0 Generic %1 scott2013nonparametric %A Scott, James G. %A Shively, Thomas S. %A Walker, Stephen G. %D 2013 %K Bayesian monotone nonparametric %T Nonparametric Bayesian testing for monotonicity %U http://arxiv.org/abs/1304.3378 %X 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.

@misc{scott2013nonparametric, 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.}, added-at = {2014-03-18T16:15:03.000+0100}, author = {Scott, James G. and Shively, Thomas S. and Walker, Stephen G.}, biburl = {https://www.bibsonomy.org/bibtex/2b7923a178f18143738cf21a31941dc99/marsianus}, description = {[1304.3378] Nonparametric Bayesian testing for monotonicity}, interhash = {959665d33447977dd64a9c7c01aa6ed0}, intrahash = {b7923a178f18143738cf21a31941dc99}, keywords = {Bayesian monotone nonparametric}, note = {cite arxiv:1304.3378}, timestamp = {2014-03-18T16:15:03.000+0100}, title = {Nonparametric Bayesian testing for monotonicity}, url = {http://arxiv.org/abs/1304.3378}, year = 2013 }