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Mathematical Sciences
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Professor Wei Liu 

Professor of Statistics

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Professor Wei Liu joined the School of Mathematics as a permanent lecturer in September 1990 immediately after finishing his PhD in statistics from Bath University, and was promoted to Senior Lecturer in 1999, Reader in 2003 and then Professor in 2005.


2005 - date Professor, University of Southampton, UK

2003 - 2005 Reader, University of Southampton, UK

1999 - 2003 Senior Lecturer, University of Southampton, UK

1990 - 1999 Lecturer, University of Southampton, UK


Research interests

My research interests include simultaneous inference, multiple testing and sequential methods. I've published more than ninety research papers in peer-reviewed international statistical journals and one research monograph, and given invited talks at many international statistical conferences. I have served as associate editor of several international statistical journals, refereed numerous papers for most major statistical journals, and served as 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 my 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 my 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 my book Liu (2010, Chapman and Hall). My 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 area of my research interests 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 most natural 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. I am 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 the maximum (or minimum) point of a function.
  • Simultaneous confidence bands for multivariate linear regression models.

Research group


Research project(s)


Design and Analysis of Experiments

Multiple Comparison Procedures

Director of Programmes of School of Mathematical Sciences

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Book Chapters

Working Papers

MATH6122 Probability and Mathematical Statistics

Professor Wei Liu
School of Mathematics and S3RI Room 9017, Mathematics Building (54) University of Southampton Southampton, SO17 1BJ Tel: (0)23 8059 8688 Email:

Room Number : 54/9017

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