The main part of my PhD thesis is on developing statistical methods to analyze stochastic processes backward from failure event. By defining the time origin for backward processes to start at failure event, questions about the trajectory of the processes leading to the failure event can be addressed. A motivating example is end-of-life-cost. Medical cost usually increases a significant portion before the end of life. By considering backward medical cost processes, we can study the systematic increase in medical cost before the end of life. We have developed nonparametric methods and regression models for analyzing backward processes. This research is under the supervision of Prof. M. C. Wang. I also work on statistical methods for prevalent cohort data, recurrent event data and recurrent measurements data.

During my undergraduate study, I worked with Prof. H. L. Yang on the problem of ruin probability (the probability that the insurance company ever has a deficit) by modelling temporal dependence of claims and income by the Granger's causal model.  We got theoretical upper bounds and recursive equation for the ruin probability.