CR Rao (1920-2023): Man of Numbers

CALYAMPUDI RADHAKRISHNA RAO, who died recently at the age of 102, was widely considered one of the foremost statisticians of his time. Not only did he make vital contributions to mathematics and statistical theory, some of which like the Cramer-Rao lower bound and the Rao-Blackwell theorem, had a far-reaching impact and became part of vari­ous graduate and postgraduate programmes across disciplines like statistics and econometrics; but he was also an institution builder, who helped build and teach statistical programmes in India and served in many government committees for the development of national statistical systems at a time when statistics as a discipline was just coming into its own in the country.

Rao was born in 1920 to the house of a CID officer in Huvina Hadagali, a town that today falls in Karnataka. He displayed, it is said, a flair for mathematics at a very early age. By six, he was reciting, by his own admission, multiplication tables right up to 20 times 20. “The teacher would line up my classmates and ask them to repeat them after me,” he once told a reporter.

Rao however hadn’t considered a career in statistics. In the early 1940s, the field was still in its infancy. The Indian Statistical Institute (ISI), the now premier institute for statistics in the country, was just a few years old, and operating out of the physics department of Presidency College in then Calcutta. Rao was in fact at that time looking to land a job in the military. World War II was still on, and Rao, a mathematics graduate from Andhra University, was travelling to Calcutta, having recently spotted an ad for the job of a mathematician for an army survey unit to work in North Africa.

Rao did not get the job, but he did manage to visit ISI, where he decided to enrol himself on a year-long training programme in statistics. Rao would go on to pursue statistics from then on, completing a Master’s programme in statistics from Calcutta University, a PhD from Cambridge, and then a long career at ISI, where he would conduct his own research, become an inspirational teacher and rise up to become its director.

Rao first created a stir in the field when he was just 24 years old. He published a paper in 1945 that demonstrated, it is said, three fundamental results that paved the way for the modern field of statistics and provided statistical tools heavily used in science today. According to the International Prize in Statistics Foundation, which awarded him the International Prize in Statistics (statistics’ equivalent of the Nobel Prize) earlier this year, “the first, now known as the Cramer-Rao lower bound, provides a means for knowing when a method for estimating a quantity is as good as any method can be. The second result, named the Rao-Blackwell Theorem [because it was discovered independently by eminent statistician David Blackwell], provides a means for transforming an estimate into a better—in fact, an optimal—estimate. Together, these results form a foundation on which much of statistics is built. And the third result provided insights that pioneered a new interdisciplinary field that has flourished as ‘information geometry’. Combined, these results help scientists more efficiently extract information from data.” In the Australian statistician Terry Speed’s words, “The 1940s were ungrudgingly CR Rao’s. His 1945 paper, which contains the Cramer-Rao Inequality, Rao-Blackwell Theorem, and the beginning of differential geometry of parameter space will guarantee that even had he done nothing else—but there was much else.”

Rao won several awards in his lifetime, from Padma Bhushan and Padma Vibhushan to the National Medal in Science (the highest award in the scientific field in the US) and the International Prize in Statistics earlier this year. He continued to remain active in this field right into his advanced age. When he found he couldn’t do much in India once he retired from the ISI, he moved to the US where he continued to teach and chair statistics departments.

With his death, the world now loses an individual who revolutionised statistical thinking.

CR RaodeathIndian Statistical InstitutestatisticsRao-Blackwell theorem