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Obituary: Professor Tze Leung Lai (1945-2023)

It is with great sadness that Professor Tze Leung LAI, a distinguished alumnus of the Department of Mathematics at The University of Hong Kong (HKU) and a world-renowned statistician, who held the position of Ray Lyman Wilbur Professor at Stanford University, passed away on 21 May 2023. Prof. Lai is survived by his wife Ms. Letitia Chow, two sons and two grandchildren.

Prof. Tze Leung Lai was born on June 28, 1945 in Hong Kong. He grew up in Hong Kong, attended North Point Government Primary School and Queen's College (which had Sun Yat-Sen as its most distinguished alumnus). Prof. Lai was admitted by the Faculty of Arts, HKU to read Economics. He changed his major to Mathematics one month after he entered HKU. Prof. Lai received his B.A. (in Mathematics, 9-Papers) with First Class Honors in 1967 and also received the Chan Kai Ming Prize and Walter Brown Memorial Prize in Mathematics in 1967. Prof. Lai then spent one year as a demonstrator of the Department of Mathematics, HKU before he went on to study at Columbia University, where he earned both a M.A. in 1970 and a Ph.D. in 1971 under the supervision of David Siegmund.

Right after he has completed his PhD degree, he was appointed as an Assistant Professor of Mathematical Statistics, Columbia University, then promoted to associate professor and professor in 1974 and 1977 respectively. He was the Higgins Professor of Mathematical Statistics, Columbia University for the period 1986-1987 before he moved to the Department of Statistics, Stanford in 1987 and became the Chair in 2001-2004. He has been the Director of the Financial and Risk Modeling Institute, Stanford University, the Professor, by courtesy, of the Institute of Computational and Mathematical Engineering, Stanford School of Engineering and the Professor, by courtesy, of Biomedical Data Science, Stanford School of Medicine since 2012, 2009 and 2015 respectively. Prof. Lai was also a Professor, by courtesy, of Health Research and Policy, Stanford School of Medicine from 2007 to 2015. The move to Stanford certainly had great influence on Prof. Lai’s research directions and industry collaborations (see in the interview by Shen, Tsang and Wong(2016): https://icsaimage.files.wordpress.com/2016/05/icsabulletin16jan1.pdf).

Prof. Lai has made fundamental contributions to mathematical statistics (including probability theory) and sequential statistical analysis, especially the development of a comprehensive theory of sequential tests of composite hypotheses. He has done ground-breaking work in (i) the solution of the long-standing "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, and (v) survival analysis. He has published over 300 papers and 12 books, and has supervised at least 75 Ph.D. theses at Columbia, Stanford, and Stony Brook and University of Padova in Italy (where he visited).

In 1983, Prof. Lai received the prestigious COPSS Presidents’ Award, the annual award given by the Committee of Presidents of Statistical Societies (COPSS) to statisticians below the age of 41 and sometimes referred as the “Nobel Prize of Statistics”. Prof. Lai is the first Chinese to have received this prestigious prize. In 1994, Prof. Lai was elected to Academia Sinica and in 2005, he received the International Chinese Statistical Association Distinguished Achievement Award and the Abraham Wald Prize in Sequential Analysis.

Together with his PhD student Chin-Shan Chuang at that time, Prof. Lai invented the hybrid resampling method around 2000, for which they developed a comprehensive statistical theory and which was independently discovered by physicists to analyze CERN’s ATLAS and CMS experiments that confirmed the existence of the Higgs boson. He has recently developed a novel Markov Chain Monte Carlo scheme that can be fully automated and has optimal statistical properties. It has many applications in science, engineering and economics.

Throughout his career, Prof. Lai maintained a strong connection to The University of Hong Kong, delivering the Y.C. Wong Lectures in Mathematical Sciences in 1989 and the C.V. Starr Lecture in Financial Mathematics in 2001. From 2003 to 2008, as C.V. Starr Visiting Professor at HKU, Prof. Lai was taking charge of the academic programs in Mathematical Finance, and very much involved with the application of statistical methods in Mathematical Statistics. During his visits through his many lectures and through conferences and workshops very often co-organized by the Institute of Mathematical Research (IMR) and the Department of Statistics and Actuarial Sciences (SAAS) at HKU, Prof. Lai brought together researchers from the mathematical and statistical communities and those working in quantitative finance, to co-develop research programs in Mathematical Statistics and Mathematical Finance. Prof. Lai continues to interact with IMR and SAAS as an advisor in proposing, coordinating and taking part in multi-disciplinary research conferences even after finishing his tenureship as C.V. Starr Visiting Professor in 2008. For example, Prof. Lai has helped IMR and SAAS to organize the HKU-HKUST-Stanford Conference in Quantitative Finance, December 9-10, 2011. Since 2011, Prof. Lai has been a member of the Advisory Committee of the Institute of Mathematical Research (IMR) and an Advisory Board Member of the Department of Statistics and Actuarial Sciences (SAAS) at HKU and played a pivotal role in fostering interdisciplinary research and collaboration in the fields of mathematical statistics and mathematical finance.

Through his many visits to HKU to help with developing research programs in Mathematics and Statistics, Prof. Lai had repeatedly expressed his love of his alma mater and Hong Kong, his reminiscence of happy times as an undergraduate here (repeated also in the two interviews: Leong(2019) https://tzelai.ckirby.su.domains/pubs/Imprints-Interview_17-Apr-2019.pdf and Lu, Small and Ying (2021) https://projecteuclid.org/journals/statistical-science/volume-36/issue-1/A-Conversation-with-Tze-Leung-Lai/10.1214/20-STS775.full), and his selfless dedication to help promote research in these subjects in Hong Kong. In fact, Prof. Lai generously donated all he earned from his C.V. Starr Visiting Professorship to the Department of Mathematics in 2009. In 2019, Prof. Lai received the Oak Anniversary Distinguished Alumni Award of the HKU Faculty of Science and he planned to give the public lecture “AI in Science and Engineering, Medicine and Finance” on February 19, 2020. Unfortunately, the lecture was postponed because of the Covid-19 pandemic and he will never be able to deliver this public lecture.

Prof. Tze Leung Lai will be remembered for his extraordinary contributions to the field of statistics, his unwavering dedication to nurturing many young statisticians, and his enduring impact on the statistics and scientific community. Although his passing leaves an immense void in the statistics community, his pioneering work and legacy will continue to inspire future generations of scholars. Our thoughts and condolences go out to his family, friends, and countless colleagues and students who had the privilege of knowing and working with him.

Tuen Wai NG
Professor
Department of Mathematics, HKU
May 23, 2023

In memory of Tze-Leung Lai

A week ago, this world lost a kind, gentle, upright and decent person; the mathematical community lost a highly accomplished but extremely modest and dedicated scholar, scientist, statistician and mathematician, who excelled in a wide spectrum of various areas of research with significant contributions in both theories and applications; those who knew him in person lost a valuable and trustworthy friend and mentor. Tze-Leung was a legendary figure and a giant in the academic world. The sudden passing in his sleep in the night of May 20, 2023 is a great and irremeable loss to this world.

Tze-Leung had been a close friend to me and Fung Kit for near to six decades ever since we were classmates as undergraduates in the University of Hong Kong. Both Fung Kit and I were deeply saddened to learn of his sudden passing. When I first heard of this sad and shocking news, I could not believe it and for a couple of hours clung to the hope that this was "faked news". For the many years I knew Tze-Leung, he was a tough and healthy chap despite his advancing years. Last month I was engaged in an exchange of emails with William Yu Sit, another good friend from our student days, about the work of the eminent mathematician-statistician C. R. Rao. Naturally, I tried to rope in Tze-Leung in the discussion, but heard nothing from him. At the time I did feel a bit worried about him. Yet, in the past couple of years in our correspondence he did not mention anything serious about his health (in his usual considerate thinking of not making others worried about him) apart from a problem with his cervical spine, which I thought arose as a result of old age and his hard work but could be treated satisfactorily, so my worry was just a fleeting thought. Little would I imagine my worry turned out to be genuine, how sad!

During the past several years with the worldwide pandemic affecting all of us, Tze-Leung and I had not met up at all. I just learnt last week that he had a stroke at home in May of 2022, stayed in a rehabilitation centre for two months but was impatient to stay inactive for that long so that he resumed working once he considered himself recovered. He even paid an academic visit to the National University of Singapore in this March, but obviously already looked fairly weak. That was exactly the Tze-Leung I have known for many years, always active in research and always ready to offer whatever help to his colleagues and younger researchers no matter what condition he himself was in. He did not live for himself but for others, a most assiduous and selfless person whom is revered by everybody. Literally speaking, he pursued mathematical research, teaching and mentoring the younger generation to the very last moment. He must have felt satisfied for what he had done when he departed, although I am sure he would continue to work equally hard had he lived on. He called himself a fighter. We can only console ourselves that this selfless fighter could finally stop fighting and rest in peace.

I took the same courses with Tze-Leung (and a group of others, some of whom become life-long friends) in my BSc Special Year in mathematics, while Tze-Leung was in his BA Final Year. One episode stood out in class of that year, which gave me an early glimpse of this upcoming academic star. In a course on algebra taught by our esteemed teacher Kam-Tim Leung, we took turns to give seminar lectures on topics assigned by our teacher. Tze-Leung offered his own proof of the structure of a finitely generated module over a principal ideal domain, complete with a lucid explanation in his animated way. I was so happy to learn that he would join us at Columbia one year after William and I were there (Tze-Leung stayed at the HKU Department of Mathematics as a tutor for the academic year of 1967-68, a story he recounted in some interviews). I went to the Kennedy Airport to meet him when he arrived and took him back to Ruggles Hall where we both resided in for the next three years. In my role as a "veteran" I showed him around New York City and the Columbia campus in the first week he arrived. He got most interested in the daily afternoon teas served in the Philosophy Hall Lounge by Faculty wives to graduate students and in the Foreign Students Office Lounge for foreign students. Later I realized his true motive, for the tea and cookies served there provided him with the necessary "fuel" for working while he skipped some meals!

Since the time we were classmates in the University of Hong Kong and later in the Graduate School of Columbia University Tze-Leung had been a close friend to me, who helped me through the ups and downs of my Columbia years with his kindness, encouragement and warm friendship. There are episodes which I always keep in my heart and shall never forget. Once his comforting words and action warmed my heart and alleviated my sorrow. It was in September of 1968 when I received a letter from home which carried the very sad news of the passing of my mother, who before her departure told my father and sister not to let me know of her passing until after the funeral so as not to cause me distraction from my study. Upon learning this heart-broken news I went to the nearby Riverside Church and sat alone in solitude for hours in that afternoon. When I returned to my small room in Ruggles Hall at dusk I found a hero sandwich in the refrigerator in the kitchen with a note of consolation from Tze-Leung. He bought me the sandwich from Ta-Kome, because he got wind of the sad news somehow and worried that I might not take in any food. What a warm, compassionate and empathizing friend Tze-Leung was.

I also remember vividly the many nights I distracted Tze-Leung from his research by going up two floors to his office in the 6/F of Mathematics Building at Columbia to knock at his door whenever I felt dejected with no progress in my work. He always readily let me in with a smile, made me feel at ease with his characteristic patience and kindness, and offered me consolatory words and helpful advice. Each time I left his office with renewed courage to go on working. I knew I had committed a "crime" of taking up his time for which he would have produced yet more important theorems. Yet, without his encouragement I might never have finished my PhD study. In one of those nights in the heated days of American campus unrest, during our chatting we heard a commotion outside and saw from the window a large group of students approaching to occupy the Mathematics Building. We quickly went downstairs just in time to climb out of the window on the ground floor to get out of the occupied building!

In the two summers of 1969 and 1970 we shared a sublet apartment (together with another undergraduate Clement Yu, who has become our life-long friend). Those months were most memorable and enjoyable, as well as the period that I made my only contribution to the world of statistics ----- to cook for T. L. Lai and feed him well and nutritiously and to provide him with the energy needed in pursuing his dedicated research throughout the night to dawn! Every single day right after dinner he would go back to his office to work; we heard the clicking sound of the key turning in the apartment door around five or six the next morning when he came back to take a nap. Around noon he would get up and left for his office again. He led a simple and austere life of an ascetic monk, as if taking a meal is only for refuelling to pursue his research work.

On a Sunday in the Spring of 1975 Tze-Leung specially made a trip to University of Miami at Coral Gables where I was teaching at the time, following a conference he attended in Tallahassee. In his usual habit of leading a simple and economical life he travelled to Miami in an overnight Greyhound bus. The long and tiring ride did not deter him from visiting me to “pre-announce” his forthcoming wedding with Letitia in June, which honestly brought me a very pleasant yet unexpected surprise, for all along I thought he spent all his time on doing research without any time for romance, forgetting that he was also a warm and caring person at the same time! As I knew quite well, he must have skipped his dinner and breakfast on the trip but subsisted only on a packet of cereal he brought on board, so I immediately took him to have a full breakfast at the University of Miami Ibis Cafeteria after picking him up at the downtown bus depot. He enjoyed the big breakfast immensely with childlike glee.

Because of the worldwide pandemic we did not meet up in the past several years as we did so frequently before. During his many visits to Hong Kong, he and Letitia would come to our home to have dinner and cheerfully consumed whatever we offered him to his heart’s content. I used to poke fun at him that he could skip several meals when he worked hard in concentration and did not want to be distracted by eating, yet he could consume a lot in a meal as if he could chew the cud (like a cow) to save the nutrient for later use! My impression of Tze-Leung is the cheerful, lively and agile chap that I knew from the Columbia days, talking with his customary enthusiasm with expressive gestures of his slender fingers. I did not see a weakened Tze-Leung after what befell him in May last year. Maybe destiny so arranged it that I keep a young and energetic image of Tze-Leung in my memory.

May this good, honest and decent man, who loved the place where he grew up in as a child and young man, and did a lot to support our local mathematical community in mathematics and statistics throughout these many years, rest in peace. In recent years Tze-Leung had more than once shared with me his view of a "recovered" HK, imbued with his characteristic optimism. One can sense his strong love for this place where he grew up in as a child and young man. I feel proud and privileged to be his life-long friend from whom I benefited much more than I can give back to him. He will be missed by many and remembered for many more years to come by a lot more people who know him by his works if not in person. Let us think more positively of the legacy he left for everybody through his deeds and his works throughout these many past years of his fulfilling life.

With our sincere condolences to Letitia, Peter and David.

Man-Keung Siu (Siu Tze)
Department of Mathematics, University of Hong Kong (retired)
May 28, 2023