Flexible prior specification for partially identified nonlinear regression with binary responses

This paper adapts tree-based Bayesian regression models for estimating a partially identified probability function. In doing so, ideas from the recent literature on Bayesian partial identification are applied within a sophisticated applied regression context. Our approach permits efficient sensitivity analysis concerning the posterior impact of priors over the partially identified component of the regression model. The new methodology is illustrated on an important problem where we only have partially observed data -- inferring the prevalence of accounting misconduct among publicly traded U.S. businesses.