Nonparametric Bayesian testing for monotonicity

TL;DR

This paper introduces two new nonparametric Bayesian tests for monotonicity, demonstrating improved finite-sample performance and extending asymptotic analysis beyond existing methods.

Contribution

It develops two novel Bayesian testing procedures for monotonicity using spline-based priors, with enhanced finite-sample results and extended asymptotic theory.

Findings

Improved finite-sample performance over existing methods

New asymptotic properties of the Bayes factor for monotonicity testing

Extension of Bayesian monotonicity testing beyond parametric models

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.