Professor Wei Liu

• Simultaneous inference (including multiple tests and simultaneous confidence bands);
• Simultaneous tolerance bands and statistical calibration;
• Tolerance bounds, tolerance regions and applications;
• Confidence sets;
• Sequential methods.

Wei's research interests include simultaneous inference, multiple testing and sequential methods, simultaneous tolerance bands, tolerance bounds/regions, confidence sets and level sets. 

Wei has published more than 120 research papers in peer-reviewed international statistical journals and one research monograph, and given invited talks at many international statistical conferences.

Wei has served as an Associate Editor of several international statistical journals, refereed numerous papers for most major statistical journals, and served as a Reviewer for grant applications and promotions in several countries.

• In many real problems, one has to make several inferences (e.g., to test several hypotheses) at the same time and it is required that the inferences are simultaneously correct `with a good chance' in certain sense. The classical problem is the comparison of several normal means. One of Wei's research interests is to devise simultaneous inferential methods that control the error probability under various definitions (e.g., Type I, Type II, Type III, and FDR) or to investigate the properties of simultaneous inferential procedures. One associated problem is to find effective methods of computing multivariate probabilities. One of his major research interests in the last few years is the construction and application of simultaneous confidence bands in regression, an overview of which can be found in his book Liu (2010, Chapman and Hall). Wei's other current research interests include statistical calibration for infinitely many future observations by using simultaneous tolerance bands, construction of confidence set for the maximum (or minimum) point of a function, and Q-Q plots.
• Another research interest is sequential methodology. In order to learn something sufficiently well (i.e., make inference about some unknown parameter(s) with a prescribed accuracy in some statistical sense), it is usual to collect information (data) sequentially. The classical problem is the construction of a prescribed 2d-wdith confidence interval for the mean of a normal population of prescribed confidence level 1-alpha, assuming the variance is unknown either. Since the variance is assumed to be unknown, it is necessary to collect observations in at least two stages. Wei is interested in devising sequential methods and studying their properties.

Research projects

• Statistical calibration and simultaneous tolerance bands: investigate simultaneous tolerance bands and construction of simultaneous calibration intervals.
• Construction of confidence sets for (sets of) parameters of interest, including the maximum (or minimum) point of a function.
• Construction of tolerance regions.
• Simultaneous confidence bands for multivariate linear regression models.