Nonparametric Bayesian testing for monotonicity

• 成果类型: Article
• 署名作者: Scott, J. G.; Shively, T. S.; Walker, S. G.
• 署名单位: University of Texas System; University of Texas Austin; University of Texas System; University of Texas Austin
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv023
• 发表日期: 2015
• 页码: 617630
• 关键词: isotonic regression

摘要

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.