Robert McCulloch's research focuses on Bayesian statistics. In the Bayesian approach, you write down a full joint distribution for all quantities of interest and then condition on the knowns. The computational revolution has made this strategy feasible in complex, high dimensional problems. Much of McCulloch's recent research is on Bayesian approaches for tree-based ensemble models. Tree based methods have emerged as a basic tool in Machine Learning because they are a relatively simple way to uncover complex nonlinear relationships in high dimensional problems.  Ensemble methods combine many tree models into one overall model which is far more powerful than any one tree model can be on its own.

Recent applications look at personalized medicine, selection of long term portfolios (pensions), and scale conversion for Marketing data.