Statistics has been called the 'poetry of sciences' and 'the soul of scientific inquiry'. It has applications across a wide spectrum of fields, leading to tangible benefits that improve the wellbeing of humanity. With the increasing role of information technology, society has been inundated by a data deluge and it is the statisticians who extract usable information from the mass of noise in these data sets.
It has been said that "A physicist solves a problem in physics using the available knowledge in physics, a chemist does the same thing in chemistry, so also a biologist and an engineer. There is nothing like a statistical problem a statistician is trying to solve with the available knowledge of statistics. His or her job is to help the scientists to solve problems in their discipline by applying available statistical methodology, but more often by developing appropriate new statistical methodology."
Perhaps the most distinguished exponent of this 'invisible science' is Calyampudi Radhakrishna Rao, a professor whose work more than 75 years ago continues to exert a profound influence. A scientist once said, "A ballet dancer gets her ovation on the spot while she is still warm from her efforts; a comedian gets his laugh across the table but a scientist must expect to wait years for his laugh." Rao was recently awarded the biennial 2023 International Statistics Prize, known as the Nobel of its field, at the age of 102.
In his remarkable 1945 paper in the Bulletin of the Calcutta Mathematical Society, Rao demonstrated three fundamental results that paved the way for the modern field of statistics and provided statistical tools heavily used in science. The first now known as the Cramer-Rao lower bound provides a means of knowing when a method for estimating a quantity is as good as any method can be. The second result named as the Rao-Blackwell theorem provides a means of transforming an estimate into a better, in fact optimal, estimate. Together, these results form a foundation on which much of statistics is built. And the third result provides insights that pioneered a new interdisciplinary field that has come to be known as information geometry. Combined, these results help scientists extract information from data efficiently. The monumental work by Rao has not only revolutionized statistical thinking in its time but also continues to exert influence on human understanding of sciences across a wide spectrum of disciplines according to the Chair of the International Prize in Statistics. Rao made distinct and extensive contributions to several branches of statistics and its applications leading to efficient methods of statistical analysis.
In multivariate analysis, one has to deal with extraction of information from a large number of measurements made on each sample unit. Not all measurements carry independent information. It is possible that a subset of measurements may lead to procedures which are more efficient than using the whole set of measurements. Rao developed a test to ascertain whether or not the information contained in a subset is the same as that given in the complete set. He also developed a method for studying clustering and other inter-relationships among individuals or populations. Using general diversity measures applicable to both qualitative and quantitative data, the method of analysis of diversity was developed by Rao for which he introduced the concept of quadratic entropy in the analysis of diversity.
Combinatorial arrangements known as orthogonal arrays were introduced by Rao for use in the design of experiments. These arrangements are widely used in multifactorial experiments to determine the optimum combinations of factors to solve industrial problems. These have also applications in coding theory. An important result of practical interest resulting from this novel approach is the Hamming-Rao bound associated with orthogonal arrays.
Born on September 10, 1920 in Huvvina Hadagall in Karnataka, Rao went to Andhra University in Visakhapatnam where he obtained his B.A.(Hons) at the age of 19. After deciding to pursue a research career in mathematics, he moved to Calcutta where he joined the Indian Statistical Institute (ISI) for training in the subject of statistics. At the same time, he completed a master’s degree program in statistics at Calcutta University. Later, Rao obtained his PhD at Cambridge University after which he became a full professor at ISI at the young age of 29.
Together with PC Mahalanobis and JBS Haldane, Rao devised the syllabi for the BStat and MStat degree courses of ISI in 1960. He included a field visit for the students to the ISI campus in Giridih for first-hand experience in conducting crop cutting experiments and collecting data for a short socio-economic survey. The syllabus also included a visit to the Central Statistical Organization for training in official statistics with a grade in a test at the end of the training. All of the students admitted to either BStat or MStat programs at ISI have received stipends during their study years. He was the Head of the Research and Training School of ISI and later its Director. Rao himself participated in teaching work at the institute. He was a strict disciplinarian when it comes to academic activities. He awarded students with a raise in stipend if they performed well but was ready to cut the stipend if the student does not perform well as per the institute norms.
I was a student of Professor Rao while doing a master’s programme in statistics at the Indian Statistical Institute and later his colleague at the Delhi Centre of the Indian Statistical Institute. I saw him for the first time in 1960 as a young student aged 17 after completing the masters program in mathematics from Andhra University in 1960. He was awe-inspiring with his international reputation for all students at ISI. Professor Rao did his M.A. in Mathematics from the Andhra University too before he went to Calcutta and Professor Vommi Ramaswamy, Head of the Department of Mathematics at the Andhra university, was his guru as well as mine.
Rao received several awards including the Bhatnagar award and the India Science award from the Government of India, the National Medal of Science from USA and was elected as Fellow of several Academies of Science in India and abroad. In total, he received 39 honorary doctorates from different universities in India and other countries. Several students received their PhD degrees under his guidance. Some of the other rare honours that CR Rao received include a National Award in his name instituted by the Government of India and a Special Postal Cover released in celebration of his 90th birthday in 2010. Rao's hobbies include photography, playing badminton, long walks and writing humorous essays.
A living legend in statistics who is still active, Rao spent forty years at the Indian Statistical Institute developing statistical activities in India before moving to the US. He is in regular touch with the activities at the CR Rao Advanced Institute of Mathematics Statistics and Computer Science (AIMSCS), Hyderabad, named in honour of him, guiding and advising the institute as well as various national and international statistical organisations and university departments of statistics. A visiting Soviet scientist who wanted to meet Dr Rao at his residence was told that he was repairing his car. The scientist met him later in his office room, saw him playing badminton in the evening and had dinner with him in the night. "I have seen the mechanic, the athelete, the scholar and the perfect host, all in one day," he said.
Rao moved to the US after superannuation in India and continued research with renewed vigour, first at the University of Pittsburgh and later at the Pennsylvania State University where he was the Director of Center for Multivariate Analysis as well as Eberly (Chair) Professor of Statistics. He is currently a Research Professor at the University at Buffalo. Rao, who will be celebrating his 103rd birthday on September 10, was honoured with the Padma Vibhushan a few years ago.
Several years ago, a passenger travelling by train to Calcutta by the Madras-Howrah Mail was asked what he did for a living. Perhaps thinking that an accurate reply would not be understood, Rao replied, "I work in a school and I am the headmaster of the school." The school is the famous Research and Training School (RTS) of the Indian Statistical Institute (ISI) and the unassuming passenger was none other than Rao who was the head of the RTS for almost a quarter of a century. We are now celebrating his work over the last 75 years which continues to exert influence. For his distinctive contributions to the field of statistics with applications in all sciences wherever data is involved, it is time that the country honours him with the Bharat Ratna.
BLS Prakasa Rao is INSA Honorary Scientist, C R Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad