R.A. Fisher's legacy in statistics

R.A. Fisher's approach to statistics can be still felt today in British statistics. His legacy has clearly lived on, such as in the distinguished history of statistics developed at the Rothamsted Agricultural Station after Fisher by Yates and J.A. Nelder. This seed of legacy has somehow spread across the US through immigration of some well-known statisticians such as G.E. P. Box.  Recently I discovered a nice article by G E P Box on R.A. Fisher,

Science and Statistics

George E. P. Box

Journal of the American Statistical Association, Vol. 71, No. 356. (Dec., 1976), pp. 791-799.

Stable URL:
http://links.jstor.org/sici?sici=0162-1459%28197612%2971%3A356%3C791%3ASAS%3E2.0.CO%3B2-W

In it, I learnt two new words,
Cookbookery and Mathematistry.Unfortunately, these two practices are still very commonly seen today.

The best website on R.A. Fisher's legacy is maintained in the Fisher Memorial Lecture page: http://www.senns.demon.co.uk/FisherWeb.html.

Ky Fan, the famous Chinese American Mathematician who's known to few Chinese people

Ky Fan (1914-2010) was a Chinese American mathematician whose accompolishments could be compared to other famous Chinese mathematicians such as Pao-Lu Hsu (1910-1970),   S. S. Chern (陈省身, 1911-2004, American mathematician and then retired in China) and L.K. Hua (华罗庚, 1910-1985). His research areas and interests were in more practical areas such as matrix theory and minimax theorems which have a lot of applications in economics and statistics. His story of not being able to return to China's Peking University to teach after the Second World War was very sad and unfortunate for China's mathematics developments, but on the other hand, it was exactly due to his stay in the US during the subsequent period that he became  a major player in modern mathematics as mathematics saw rapid developments in such areas such as game theory, statistics and operation research, in which Ky Fan made a lot of contributions following the footsteps of Jon von Neumann and Hermann Weyl. He was a student and collaborator of M Frechet and they co-authored a book in 1946: Introduction a la Topologie Combinatoire. (Its English translation was published in 1967 and recently reissued by Dover under the title: Invitation to Combinatorial Topology.)

Ky Fan's work was characterized by its wide influence in many areas, and was widely cited and studied by other researchers, see for example references 1, 2, 3. His results were quoted as classic theorems in many textbooks. His practical interests were probably maintained by his frequent visits during 1947-1960 to national laboratories such as the National Bureau of Standards, see ref.4.

Ky Fan was born in Hangzhou, China on September 19, 1914. He enrolled in Peking University in 1932, and received his B.S. degree from Peking University in 1936. Fan went to France in 1939 and received his D.Sc. under Frechet from the University of Paris in 1941. A member of the Institute for Advanced Study in Princeton from 1945 to 1947, he then joined the faculty of the University of Notre Dame, eventually becoming full professor. In 1965, Fan became professor of mathematics at UC Santa Barbara, retiring in 1985.

Fan was elected an Academician of the Academia Sinica (Taipei, Taiwan) in 1964. Fan served as the director of the Institute of Mathematics there from 1978 to 1984.

A short biography of Ky Fan is given in Ref.5. A nice Chinese article about him was written by his last student, ref.6.

1. Ky Fan Inequalities: http://arxiv.org/PS_cache/arxiv/pdf/1108/1108.1467v2.pdf
2. On a Minimax Inequality of Ky Fan. http://www.jstor.org/stable/2046475
3. On the Ky Fan Inequality and Related Inequalities II. http://www.austms.org.au/Publ/Bulletin/V72P1/pdf/721-5068-NeSa.pdf
4. Some Metric Inequalities in the Space of Matrices. http://www.ams.org/journals/proc/1955-006-01/S0002-9939-1955-0067841-7/S0002-9939-1955-0067841-7.pdf
5. Every Waking Moment Ky Fan (1914-2010): http://www.ams.org/notices/201011/rtx101101444p.pdf
6. 记恩师樊畿教授 http://news.sina.com.cn/c/2007-05-17/110213011025.shtml

Wither Mathematical Statistics?

Herbert Robbins wrote (or talked) a nice reflection on the state of mathematical statistics in 1975, published a paper under this title in Advances of Applied Probability, Vol.7. This was probably at the end of golden years of theoretical statistics, some of this history also captured nicely in the very entertaining book by E.L. Lehmann, Reminiscences of a Statistician: the Company I Kept, published by Springer 2008. Mathematical statistics (ms) probably came out of the need to provide the rigor and theory for data analysis and data collection in the period of agricultural boom in the hands of R.A. Fisher, E.S. Pearson, Jerzy Neyman, etc, and was probably well justified to boom right after demonstrating its usefulness during the second world war along with the birth of operation research. But this inward-looking and self-indulged developments, though productive, probably the golden years in statistics, but by 1975, the initial excitement seemed to have run out of steam and it is in need of new air and fresh ideas. It is interesting to the reflections  from one of the major figures in modern statistics on the future of  ms at the time. He is probably not alone, as John W. Tukey had said the same thing earlier many times, such as in the earth-shaking article: The Future of Data Analysis, published in 1962, Annals of Mathematical Statistics. Apparrently there had been a disconnect between the development of mathematical statistics and data analysis. That was bad, as mathematical statistics was supposed to help "doing data analysis", not being done as another branch of mathematics.  This was an unfortunate development, since its founding fathers like Harold Hotelling and Abraham Wald, among others, many of whom have both applied roots such as economics but would like to see statistics as an integral but independent component of the scientific discipline, not just a subdiscipline sitting within a mathematics department. Ironically, whether it is C. Stein's breakthroughs or systematic efforts such as the 1970s robustness studies, they all proved  that the optimality of statistical procedures is more an illusion than something can be achieved remotely in practice. Now in the new century, the tide has completely changed with the waves of problems in biology and medicine such as imaging and if statisticians cannot face up to the task of the new digital era, and many others such as engineers and computer scientists will gladly do the work instead. Today it will be surprising to find any modern statistician who is not involved in some kinds of real application areas, whether climate, environment or clinical trials. Statisticians nowdays need to know more than a few areas, including many statistical methodologies  and theories, so that,  when faced with a consulting problem from a scientist colleague, they do not have to take on Robbins' advice of following the Hippocratic Oath and do no harm, they can actually make inroads into some potentially new areas.

References:
1.J. W. Tukey (1962), The Future of Data Analysis, Annals of Mathematical Statistics.
2. 陈希孺: 数理统计学:世纪末的回顾与展望, 统计研究, 2000 年第2 期.

关于我国数理统计学发展中存在的问题的几点思考, 北京统计, 2003年.

Getting to know Ming Chen Wang (王明贞)

I was sitting in front of a nice little old book: "Selected Papes on Noise and Stochastic Processes", edited by Nelson Wax, 1954, published by Dover Publishing. In it contained were several nice review articles on Brownian motion, one of which was by Ming Chen Wang and G.E. Uhlenbeck, On the Theory of the Brownian Motion II, reprint from Reviews of Modern Physics, 1945. Who is Ming Chen Wang and where is he or she now?

It turned out that Ming Chen Wang has a Chinese name, 王明贞, who was a little-known physics professor at Tsinghua University since 1955 in Beijing, China. Except for 7 years in prison apparently due to her husband's connection to Jiang Qing, one of the Gang of Four and Chairman Mao's wife during 1966-1973, she taught physics to China's students, just like many other teachers, and until 2010 when she died at the age of 104. 

The only English account I can find of her is here:  https://sites.google.com/site/kaizhangstatmech/chinese-scientists/mcwang.  She was one of the pioneers in women in sciences, and it took her a lot of efforts to obtain an opportunity to go to college and years of work in order to go to abroad for further study. Her PhD was obtained in 1942 (at the age of 36) in physics at the University of Michigan, with a thesis: A Study of Various Solutions of the Boltzmann Equation. Her employement history was a little strange, she worked at MIT as a research scientist for a few years, then she went back to China, worked as a professor at Yunnan University till 1949. Then, suddenly, right before China was liberated, she went back to US to work at the University of Notre Dam for a few years until 1953, when she decided to go back to China again. She succeded in 1955 to return to China. My guess is that, as a woman, she needed to follow her husband in her moves and also in consideration of her other relatives such as her brother, who was more famous as a physicist and later as a goverment official at the same time in the US. But for her career, too many moves may not be too good. On the other hand, after arriving at Tsinghua University in 1955, due to New China's in education and everything at the beginning of developments, and influences from the Russia, she did not continue her research career at all and she devoted all her time to education. (Actually she was able to teach from 1955-1966, and due to imprisonment from 1966-1973, she did not resume her academic work and retired in 1976, see ref.1.) In recent years she finally got some well-deserved recognition from her university and colleagues, and she was bestowed with some high honors, even being called China's Madam Currie (which may be a little exaggerated), and maybe  China or Tsinghua U. has finally realized what they have missed over these many chaotic years after all!
Reference: see also, 1. 王明贞：转瞬九十载, 物理,
2. 布朗运动理论一百年
郝柏林, 2011, 物理,
40卷, 第一期

Mathematical Modeling of Intracellular Movements

Nice group photo from the NIMBioS workshop Mathematical Modeling of Intracellular Movements, which was held on October 24-26, 2011 at NIMBioS. I was the one on the far right. The workshop was held in one of the newest NSF mathematical research insititutes, call National Institute of Mathematical and Biological Synthesis, housed on the campus of the beautiful University of Tennessee, Knoxville campus. We were put in a nice hotel right next to the World Fair park, which had been built for the 1982 World Fair (Expo), which happened to be the first World Expo that PRC ever participated. The park was surpringly well-maintained ---if you walk through the park, you may feel as if the World Fair (Expo) just happened yesterday. The city of Knoxiville has a nice downtown area with lots of nice restaurants, and also an interesting historical district which is not too far from the downtown. The river and the railway along the river is definitely a scence not to be missed by any causal visitor. The workshop itself turned out to be very successful and fruitful. There are lots of young people and you can sense the excitement at the threshold of a new era in biology based on quantitative techniques and exciting high resolution and real-time measurements. There are very nice interactions and very interesting discussions on the interfaces of mathematics and biology (mainly plant science), including live cell imaging, microtubule modeling, measurement of intracellular movements (diffusion), and surprisingly shape (geometry) plays an important role in many of these problems.  

Empirical Bayes Approach: the future for statistical inference?

I attended a surprising event on October 19, 2011 at the American Film Institute Silver Theatre in Silver Spring, Maryland. The event was not to see a movie star, but on the other hand, the surprisingly small audience was treated to a event of great star power in the statistical sense, as the symposium honoree Brad Efron, aka the bootrap fame, and also with many other notable roles such as in the play for empirical Bayes and the geometry of likelihood, shined brightly once again. Like always, he gave with an inspirational talk on Bayesian Inference and the Parametric Bootstrap, with a beautiful handout on his slides. He concluded by remarking that improper Bayesian approach should always be evaluated via the frequentist approach. (Jim Berger may be smiling somewhere!)

I remember when first starting graduate school at UNC, Chapel Hill, Brad Efron was invited to give the prestigious Hotelling lecture, and one of his handout was: Why Isn't Everyone a Bayesian? http://www.jstor.org/stable/10.2307/2683105. Now almost 25 years later, Bayesian is really making a comeback. Indeed, just two days later, Sharon B. McGrayne, author of the book: The Theory Would not Die, How Bayes' Rules (Changed the World, my ed) gave a talk at my institute to a surprisingly packed audience of mostly physical scientists, engineers.
Indeed, for Bayesian statistics to be used seriously in practice, such as for uncertainty analysis in metrology, http://www.nist.gov/pml/pubs/tn1297/index.cfm, there is still a long way to go:  how to validate and how to relate to classical and traditional ways of uncertainty assessment. Can confidence intervals traditionally being derived based on clasical statistics and frequentist interpretation be really replaced by Bayesian inference? Why and how to make it routine in practice?
Reference: Efron, Bayesian Inference and parametric bootstraphttp://stat.stanford.edu/~ckirby/brad/papers/2011BayesianInference.pdf

Chaos: the Science of Predictable Motion

This is the title of a book by Richard Kautz. A former Nist colleague, this is a nice account of chaos, in an informal style, but still enough technical details. The most interesting part is the account of Josephson effect and voltage standard development, in which chaos plays an important role in understanding the measurement uncertainty, and in the design of voltage standard, because the mechanism is similar to a pendulum (its chaotic attractor is shown in the picture above).  Kudos to the author for writing an entertaining book.

My own involement with chaos started with my thesis work on chaotic time series. I think one of the famous pictures I developed was the study of predictability of the 3-var Lorenz system (see the picture above, published figure in black and white in Ref 2). I had a few chances to see and talk to E. N. Lorenz while at NCAR. In particular, Lorenz himself continued his work on developing on "toy" examples of simple chaotic models for important experimental and theoretical studies, one of which is the 40-var model he developed around 1996. This model was used in targeted observations study by him and immediately by myself when Berliner and I proposed a Bayesian statistical design framework for the targeted observations problem, On the broader scale, I think chaos theory is nice, in that it connects random and statistical theory to dynamical systems, which are the typical models for physics and sciences. Examples are odes, and mapping in the discrete-time case. After 30 years or so developments of chaos theory in many areas, mostly in mathematics and physics, I think the most promising future developments may lie in the application of chaos theory to emerging areas such as biology or nanotechnology.
References: 1. Richard Kautz, Chaos: The Science of Predictable Random Motion, Oxford University Press, 2011. 2. Zhan-Qian Lu, R.L. Smith, Estimating Local Lyapunov Exponents. In pp.135-150, Nonlinear Dynamics and Time Series. Building a Bridge Between the Natural and Statistical Sciences. Eds Colleen D. Cutler and Daniel T. Kaplan, American Mathematical Society, 1997.