Bayesian Statistics

Bayesian statistics is a statistical theory based on the strategy for minimizing the expected loss to provide the basis for rational decision making in the context of uncertainty. The uncertainty is measured by probability of an event, and the degree of uncertainty may be based on prior knowledge and experts’ beliefs about the event. Bayes’ Theorem, named after Thomas Bayes, plays the central role in computing and updating conditional probabilities after more evidence or information becomes available.In modern statistics, Bayesian method has been widely used in clinical trials, genetics, disease mapping, environmental epidemiology, biomedicine, and public health research.

Our Research:

• Gwon, Y., Mo, M., Chi, Z., Chen, M.-H., Li, J. Xia, A., and Ibrahim, J. G. (2020) Network Meta-Regression for Ordinal Outcomes: Applications in Comparing Crohn’s Disease Treatments. Statistics in Medicine, 39: 1846-1870.
• Ibrahim, J. G., Chen, M.-H., Gwon, Y., and Chen, F. (2015). The Power Prior: Theory and Applications. Statistics in Medicine, 34: 3724-3749.
• Ibrahim, J. G., Gwon, Y., and Chen, MH. (2015) “Bayesian Survival Meta-Experimental Design Using Historical data”, In: Modern Approaches to Clinical Trials Using SAS: Classical, Adaptive, and Bayesian Methods. Edited by S. M. Menon and R. Zink. Gary, NC: SAS Institute Inc., pp 107-131.
• Zhang, P., Liu, J., Dong, J., Holovati, JL., Letcher, B., and McGann, LE. (2012) A Bayesian adjustment for multiplicative measurement errors for a calibration problem with application to a stem cell study. Biometrics, 68(1): 268-274.
• Yu F., Chen M.-H., Kuo L., Peng H., and Yang W. (2011), Bayesian Hierarchical Modeling and Selection of Differential Expression Genes for the EST Data, Biometrics, 67(1): 142-150.
• Yu F., Chen M.-H., and Kuo L. (2008) Detecting Differentially Expressed Genes Using Calibrated Bayes Factors, Statistica Sinica, 18: 783-802.
• Zhang W., Chaloner K., Cowles, MK., Zhang Y., and Stapleton JT. (2008). A Bayesian pooled analysis of doubly censored data using a hierarchical Cox model. Statistics in Medicine. 27: 529-542.
• Meza JL (2003). Empirical Bayes Smoothing of Relative Risks in Disease Mapping.  Journal of Statistical Planning and Inference. 112: 43-62.