C R Rao turns 100: A statistician by chance

“If there was a Nobel Prize for mathematics and statistics, he would have won it decades ago,” has been a common refrain whenever the name of Calyampudi Radhakrishna Rao, or C R Rao, is mentioned in scientific circles. His contributions to statistics and to mathematics, spanning 80 years and counting are unparalleled.

C R Rao is considered the greatest living statistician. He celebrated his 100th birthday on September 10. He continues to be active at this ripe age, contributing to contemporary subjects like big data, epidemiology and neural networks by way of editing of handbooks in collaboration with statisticians. 

Former US president George W Bush described Prof C R Rao as the “Prophet of a New Age” in a citation while presenting him the President’s Medal, the country’s highest award to a scientist in 2003. 

In an amazing coincidence, during his first 40 years of work from 1940 to 1980 in India at the Indian Statistical Institute (ISI), C R Rao published over 250 scientific papers; over the next four decades too, based in the US, he has contributed an equal number.

Data and COVID-19

Wherever data is used, C R Rao’s imprint will be felt. His path-breaking research work transcends subjects from statistics to genetics, chemistry, physics, archaeology, economics and some emerging areas too. Statistics and modelling are the backbone of Big Data and large number crunching which is revolutionising several fields and accelerating large projects. 

In the past few years he has edited Handbook on Epidemiology with Arni Srinivasa Rao of the University in Georgia. Srinivasa Rao has worked extensively on statistical modelling of infectious diseases like HIV/AIDS and is also from the ISI.

Srinivasa Rao and Prof Steven Krantz of the University of Washington have used mathematical modelling to compute realistic pictures of the coronavirus infection in several countries, including India. Typically, a model can be used to carry out a biological experiment using computers instead of laboratories to understand the progression of diseases and make predictions.

According to Prof BLS Prakasa Rao, an INSA chair at the Dr C R Rao Institute in Hyderabad, “His monumental work done as early as 1943-45, popularly known as Cramer-Rao Inequality are still cited extensively today.”

Prakasa Rao, a student, colleague and former director of ISI Kolkata, who takes pride in describing himself as a fan of Dr C R Rao, says, “At ISI, he traversed all responsibilities of teaching, research and administration to rise as director in 4 decades. When he took mandatory retirement at age 60 in 1980, Dr Rao had published an astonishing 201 research papers and etched an indelible mark."

Thereafter, he moved to the US with a professorship at the University of Pittsburg and then to  Pennsylvania State University till 2008. At present he holds a professorship at the University of Buffalo.

C R Rao, Mahalanobis and Planning

If Prof Mahalanobis is the father of statistics and planning in India, his most distinguished student, Dr C R Rao was instrumental in extending and strengthening their use through the formative stages of the Central Statistical Organisation (CSO) and the many state bureaux of statistics. Similarly, the creation and evolution of the NSSO, which is the backbone for generating data to plan economic growth, is owed to Dr Rao and his students.

Incidentally, it was in 1946 that Prof Mahalanobis, sent C R Rao to do a project for Oxford University's Department of Anthropology related to analysing measurements made in human skeletons obtained from Jebel Maya in North Africa to trace their origins. It was a turning point in his career.

Rao not only did a creditable job but got a chance to work with the renowned Sir Ronald A Fisher to do his Ph.D. too. 

Early groundbreaking work 

But as history bears out now, his most important and pathbreaking work which is termed as the Cramér-Rao inequality and a set of papers were published while working at the Department of Statistics, Kolkata University and later at ISI. All of this before turning 26 and obtaining a PhD in 1948 from Cambridge.

Several of these seminal contributions find a place in textbooks with Rao prefixed. For example the theorems referred to as Rao-Blackwellization, the Cramér–Rao bound, Fisher-Rao etc to a dozen other concepts – Rao Distance, Rao’s Paradox, Neyman Rao Test were all done during this extraordinary phase.

It was in the early 1970s that Cambridge University awarded him an Sc.D. degree and made him an Honorary Life Fellow of King’s College, Cambridge.

Several textbooks on statistics carry Dr Rao’s name and work. He himself has authored 14 books.

 It’s interesting to note that the first half of the 20th century belonged to statistical theory. Several Indians too figured in the list of giants like PC Mahalanobis, Debabrata Basu, Jayanta Kumar Ghosh, Pranab K Sen, etc. 

Models and Applications

While a large part of his research work concerns theoretical aspects, there have been practical applications in recent years. Rao’s most widely regarded work on Multivariate Analysis has found utility in economic planning, weather prediction, medical diagnosis, tracking the movements of spy planes, and monitoring the movements of spacecraft.

In industrial settings his research in combinatorial mathematics helps in the design of experiments among which Orthogonal Arrays are the most prominent. They are being described as the new mantra in large industries globally, which enable the determining of size, location and environmental aspects in design.   

Statistician By Chance

 In an autobiographical work titled Statistics as a Last Resort, C R Rao himself describes his entry into statistics as a chance happening. The story goes that the young Rao, brimming with excitement and armed with a BA (Mathematics) from Andhra University and looking for a job in North Africa, arrived in Kolkata for an interview in 1940. Somehow, the global job eluded him but brought him into contact with one Mr Subramanian, who was training at the Indian Statistical Institute (ISI), Calcutta. Influenced by the conversation, he joined the course. There was no looking back after that.

That accidental event began the association of Rao with ISI. Thereafter for four decades, his stellar work and growing contributions in statistics made him synonymous with ISI. His work got global recognition personally and for the institute.

That he was a ‘bright spark’ in math was evident from his early days at school and college in Andhra Pradesh, where solving tough problems was his forte. Rao was born in Huvvina Hadagalli village in Karnataka to C Doraiswamy Naidu, a police official and Laksmikanthamma on September 10, 1920. However, his father’s transfers took him to different places in Andhra Pradesh, before settling down in Visakhapatnam.

C R Rao Institute

In 2009, Rao went to Hyderabad and with the help of fellow statisticians he worked on establishing a research institute to promote mathematics, statistics and computer science. In addition to liberally funding the venture he could obtain generous grants from the government under prime minister Manmohan Singh. The University of Hyderabad gave a few acres of land.

The C R Rao Institute is now functional and also a road has been named in honour of the great statistician. Efforts to establish a musuem named Sankhya are on.