Stochastic Modeling

A stochastic process is a random process changing over time. It is well-suited for modeling dynamic and complex biomedical processes. Combined with other statistical theories and methodologies, stochastic modeling can bring us unique insight into these processes. An interesting application is the modeling of panel count data, in which a counting process is observed at a number of discrete time points during a study where subjects may have different number of observations at different time points.

Another example of stochastic modeling is the study of multi-states of disease progression, in which the transition from one disease state to others is a study of interest. In biomedicine research, stochastic modeling plays a critical role in ascertaining the disease progression and in assessing an intervention effect on slowing down the disease progression. 

Our Research: 

• Bakoyannis, G., Zhang, Y., and Yiannoutsous, C. (2019). Nonparametric inference for Markov process with missing adsorbing state. Statistica Sinica. 29: 2083-2104.
• Zhu, L., Zhang, Y., Li, Y., Sun, J., and Robison, L. (2018). A semiparametric likelihood-based method for regression analysis of mixed panel-count data. Biometrics. 74: 488-497.
• Zhao, XQ. and Zhang, Y. (2017). Asymptotic normality of nonparametric M-estimators with applications to hypothesis testing for panel count data. Statistica Sinica. 27: 931-950.
• Hua, L. and Zhang, Y. (2012). Spline-based semiparametric projected generalized estimating equation method for panel count data. Biostatistics. 13(3): 440-454.
• Cheng, G., Zhang, Y., and Lu, L. (2011). Efficient algorithms for computing the non- and semi-parametric maximum likelihood estimates of panel count data. Journal of Nonparametric Statistics. 23: 567-579.
• Lu, M., Zhang, Y., and Huang, J. (2009). Semiparametric estimation methods for panel count data using monotone B-splines. Journal of the American Statistical Association. 104: 1060-1070.
• Wellner, JA. and Zhang, Y. (2007). Two likelihood-based semiparametric estimation methods for panel count data with covariates. Annals of Statistics. 35: 2106-2142.
• Zhang, Y. (2006). Nonparametric K-sample tests with panel count data. Biometrika. 93: 777-790.
• Zhang, Y. (2002). A semiparametric pseudolikelihood estimation method for panel count data. Biometrika. 89: 39-48.
• Wellner, JA. and Zhang, Y. (2000). Two estimators of the mean of a counting process with panel count data. Annals of Statistics. 28: 779-814.