Empirical Bayes with Trees

The research project focuses on the estimation of parameters in a non-linear y model, where the observables x and y are determined by an unobserved variable theta generated by a prior. In such cases, the traditional method of using the posterior mean of theta to run regression against y, which is accurate in linear models, may result in biased estimation. To address this issue, we propose a new method with its statistical properties and simulation examples. This project aims to improve parameter estimation in non-linear models under Empirical Bayes context and compare the performance with non-parametric methods.