Tze Leung Lai, the Ray Lyman Wilbur Professor of Statistics at Stanford University, passed away on May 21, 2023, at the age of 77. He made far-reaching contributions to sequential statistical analysis and a wide range of applications in the biomedical sciences, engineering and finance. Tze received many honors for his research, including being the first Chinese recipient of the COPSS Award and an elected member of Academia Sinica. Tze also had a positive influence on many students, colleagues and friends through his infectious love of research, institution building and kindness.

Tze was born on June 28, 1945, in Hong Kong, where he grew up and attended The University of Hong Kong, receiving his B.A. degree (First Class Honors) in Mathematics in 1967. He went to Columbia University in 1968 for graduate study in statistics and received his PhD in 1971 with David Siegmund advising his dissertation. He stayed on the faculty at Columbia and was appointed Higgins Professor of Mathematical Statistics in 1986. A year later he moved to Stanford where he remained for the rest of his career. He was the chair of the Stanford Statistics department from 2001–04.

Tze made many fundamental contributions to sequential statistical analysis such as the development of a comprehensive theory of sequential tests of composite hypotheses that unified previous approaches and far-reaching extensions of sequential statistical methods to cope with practical complexities that arise in changepoint detection in engineering and group sequential clinical trials in medicine. He also did groundbreaking work in areas such as (i) the multi-armed bandit problem; (ii) stochastic approximation and recursive estimation; (iii) adaptive control of linear stochastic systems and Markov decision processes; (iv) saddlepoint approximations and boundary-crossing probabilities in Markov random walks and random fields; (v) survival analysis; (vi) inference for hidden Markov models; and (vii) fundamental contributions to probability theory such as establishing the law of the iterated logarithm for Gaussian processes, characterizing the limit set to be the unit ball of the corresponding reproducing kernel Hilbert space.

In his early years on the faculty at Columbia, Tze focused entirely on methodology and theory, but when teaching a new course on time series, he was asked to be a statistical consultant for a medical project involving time series about sudden infant death syndrome. This marked the beginning of an enduring interest in multidisciplinary research and prolific contributions in a wide range of areas including medicine, engineering and finance. This was reflected in the many roles he was playing in multidisciplinary institutions at the time of his passing, including founder and leadership roles: founder and director of Financial and Risk Modelling Institute; co-founder and co-director of the Center for Innovative Study Design; co-director of the Biostatistics Core of the Stanford Cancer Institute; core member of the Center for Innovation in Global Health, Center for Precision Mental Health and Wellness, and Center for Population Health Sciences in the School of Medicine; and faculty affiliate of the Doerr School of Sustainability & Climate Change.

In addition to the institution building Tze did at Stanford, he did much institution building in China. He was the C.V. Starr Visiting Professor at Hong Kong University (HKU) from 2003–08 where he developed programs in mathematical statistics and mathematical finance (Tze donated all his earnings from the visiting professorship to HKU’s Department of Mathematics); the honorary dean of the Center for Financial Technology & Risk Analytics at Fudan University; a visiting chair professor of Southwestern University of Finance and Economics; and an advisory committee member of the Yau Center for Mathematical Sciences at Tsinghua University, the Center for Statistical Science at Peking University, the Department of Statistics and Actuarial Science at the University of Hong Kong and the Institute of Statistical Science, Academia Sinica.

Tze launched the careers of a tremendous number of students, advising 79 PhD dissertations. Tze was beloved by his students for his care and devotion to us. He could be frustrating to work with, though. This combination is captured in his relating of his experience with his student Milan Shen in her, Ka Wai Tsang and Samuel Po-Shing Wang’s “Conversations with Tze Leung Lai” (ICSA Bulletin, January 2016). Tze had suggested to Milan an ambitious dissertation topic which it appeared would take two more years to complete, but when Milan received a job offer from Airbnb that would require her to start in eight months and she was worried that she would not be able to complete her dissertation in time, Tze told her to go ahead and accept the offer as he knew it was a good opportunity for her. Tze recalled to Milan what happened thereafter, “[When under stress, it is important] to have a firm grasp of one’s constraints and to optimize subject to the constraints. Of course the constraints are often time-varying, and that is why you found me repeatedly ignoring the date (the end of August) you had to show up at Airbnb until late July when I began to take it seriously. In other words, I do not want to restrict creativity by these constraints until they become real. This is also consistent with my philosophy of adaptation in study design, statistical analysis and dynamic optimization.” When one of us (Dylan) was just midway through working on his dissertation, Tze emailed from a trip to Hong Kong to tell me to please finish up my dissertation work in the next three weeks before he returned as he wanted us to focus on some new directions he had developed during his trip. After a frantic three weeks in which I of course didn’t come close to finishing my dissertation, Tze returned and I worriedly showed him what I had done. He had forgotten about telling me to finish up my dissertation and what the new direction he was thinking we would pursue, but laughed and said that if he hadn’t told me that, I wouldn’t have gotten so far while he was gone. However frustrating his changes in direction could sometimes be, it was hard to stay mad at him as he could laugh at himself and it was always clear he had our interests at heart. Even after we graduated, Tze could always be counted on for help if we needed it and continued caring for our postdoctoral career development. One of us (Zhiliang) recalled his memorable experiences of visiting Tze in the summer after his PhD: “He invited me to visit Stanford for a month to finish a few papers, suggesting that I stay in his house. It was such a generous offer, and a wonderful experience for me. I still think it’s the most productive month I have ever had although I felt a little guilty as I literally took over the living room for the entire month. His family, especially his mother, were so kind and treated me so well.”

Beyond his students, Tze provided guidance and support to many others. He was full of smiles and encouraging stories, and helped junior researchers to make collaborative connections. Since his passing, comments have poured in remembering Tze’s positive impact. Some examples are “It is hard to think of what my early years as a scholar would have been without his support and encouragement,” and, “I am extremely saddened by the news. Professor Lai was instrumental and supportive in my entire career.” Tze had a big heart when he thought someone needed help. When one of us (Dylan) described to Tze how a former student of my own was having a problem that his strong work was not being appreciated by his department chair for political reasons, Tze dropped everything to talk to my former student and came up with a bewildering range of practical (as well as impractical) suggestions to help.

Tze was legendary for his hard work and work habits. After often spending the day in back-to-back meetings when he wasn’t teaching, he would have a light dinner and then go the Stanford math library (if you couldn’t find Tze, you knew to look for him in the math library and he would always make time for you). After the library closed at 9pm, it was back to his office to work. When one of us (Dylan) was a graduate student, I noticed one summer that Tze seemed to be staying in the department even later than usual, until around 1 or 2am. I met him walking out of Sequoia Hall late one night and mentioned that he seemed to be working unusually hard lately and maybe he should try to take it a little easy. He responded happily that usually his wife Letitia would pick him up because their son was using their other car and she did not want to pick him up past 10pm so she could sleep, but with his son away that summer, he could drive himself and stay as late as he wanted.

Tze is survived by his wife of 48 years Letitia, his two sons David and Peter, his two daughters-in-law Crystal and Iris, his two grandchildren Valerie and Kit and his sister Anna. Tze told one of us (Dylan) that his proudest achievement was raising his two sons David and Peter. David said, “My dad wasn’t the type to coach our Little League teams due to his busy academic schedule but he was very dedicated to us in his own way.” When they were in elementary school, Tze would take David and Peter after dinner to Stanford’s Green Library where he would do his work and make sure they did their homework, bribing them by taking them to the store to get candy bars they couldn’t have at home. David remarked that at the time he thought it was normal for eight-year-olds to go to Green Library, but now as a historian who works a lot at Green Library, he realizes there aren’t any other eight year olds there.

When Tze passed away unexpectedly, the heartbreaking news quickly spread around the world. Tze’s energy, brilliance and kindness will be sorely missed, but will live on through the many in the statistical community on whom he had a positive influence, and the institutions he has built.

Written by Ying Lu, Stanford University; Dylan Small, University of Pennsylvania; and Zhiliang Ying, Columbia University.

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