Bayesian Nonparametric Monotone Regression
Abstract
In many applications there is interest in estimating the relation between a predictor and an outcome when the relation is known to be monotone or otherwise constrained due to the physical processes involved. We consider one such applicationinferring timeresolved aerosol concentration from a lowcost differential pressure sensor. The objective is to estimate a monotone function and make inference on the scaled first derivative of the function. We proposed Bayesian nonparametric monotone regression which uses a Bernstein polynomial basis to construct the regression function and puts a Dirichlet process prior on the regression coefficients. The base measure of the Dirichlet process is a finite mixture of a mass point at zero and a truncated normal. This construction imposes monotonicity while clustering the basis functions. Clustering the basis functions reduces the parameter space and allows the estimated regression function to be linear. With the proposed approach we can make closedformed inference on the derivative of the estimated function including full quantification of uncertainty. In a simulation study the proposed method performs similar to other monotone regression approaches when the true function is wavy but performs better when the true function is linear. We apply the method to estimate timeresolved aerosol concentration with a newlydeveloped portable aerosol monitor. The R package bnmr is made available to implement the method.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2006.00326
 Bibcode:
 2020arXiv200600326W
 Keywords:

 Statistics  Methodology;
 Statistics  Applications
 EPrint:
 Environmetrics 2020