Flexible regression modelling under shape constraints

Abstract This chapter presents methodology for estimating the posterior distribution of regression models subject to shape constraints. There is a specific focus on estimating and performing covariate selection for monotonic polynomials, however the computational and methodological techniques are more widely applicable. We demonstrate our methodology on a number of simulated and real-world data sets. Our covariate selection code is available as an R package at https://github.com/hhau/rjmonopoly .