Postulating monotonicity in nonparametric Bayesian regression
Seminar Room 1, Newton Institute
Strong structural assumptions, such as constant proportionality between hazard rates in analyzing survival data, or similar proportionality between odds when considering binary responses, are often imposed on the form of the regression function describing the effects of the covariates on a response. This is typically done as a modelling convention and without real support from contextual substantive arguments, evidence coming from earlier studies, or careful diagnostics afterwards. Here we consider one particular way of relaxing such assumptions, by postulating that the dependencies between the considered response and at least some of the covariates are monotonic in an assumed direction. We then consider a class of constructing such models, based on an extension of piecewise constant functions into the multivariate case. Applying Bayesian inference and MCMC, we then illustrate the method by an epidemiological study of some risk factors for cardiovascular diseases.