Statistics legend C.R. Rao passed away. He witnessed the century-old history of statistics

The legendary master of statistics C. R. Rao has passed away at the age of 102

Anyone who has studied statistics will be familiar with his name——

The Cramér-Rao inequality is based on He is named after Harald Cramér. The sentence he wrote on the title page of "Statistics and Truth" is widely circulated in the Chinese world:

In the ultimate analysis, All knowledge is history;

In an abstract sense, all science is mathematics;

In a rational world, all judgments are statistics.

From 1920 to 2023, Professor Rao’s life was almost synchronized with the entire development history of modern statistics

In 2021, an article was published in " An article in the International Statistical Review evaluated his life as "a century of statistics"

His career is closely related to the history of modern statistics, covering everything from Pearson and Fisher The development of the era of big data and artificial intelligence

Legendary statistician

Mr. Rao was born in India in September 1920

His statistical career It started in the 1940s: First, he obtained a master's degree in mathematics from Andhra University and a master's degree in statistics from the University of Calcutta in 1943, and then went to King's College, Cambridge University, England to study for a doctorate, studying under one of the founders of modern statistics. Ronald Fisher

.

At the beginning, Rao had already shown extraordinary talent

In 1943, he passed his master's thesis in statistics at the University of Calcutta with a score of 87%. This record has not yet been broken by Calcutta University. The reviewers also rated this paper as "PhD level"

In 1945, Rao, who was only 25 years old at the time, published an important statistical paper "The Credibility of Information and Statistical Parameter Estimation". Reaching accuracy"

In this paper of just 10 pages, Rao proved the

Cramér–Rao inequality

and the

Rao-Blackwell theorem. Both are important components of modern statistical methodology. Cramér-Rao inequality provides a lower bound on the error for unbiased parameter estimation, providing a benchmark for the performance of the estimator. The variance of any estimator cannot be lower than this lower bound

The Rao-Blackwell theorem describes how to transform an arbitrary rough estimate into an estimate that is optimized by the mean square error criterion or similar criteria. The core idea is to use the effective information in the data for estimation, which is better than using all the data directly.

This paper also lays the framework for the information geometry theory. Information geometry is widely used in current artificial intelligence research, and has also been used for the measurement of the Higgs boson at the Large Hadron Collider

Specifically:

Rao introduced the concept of distance or divergence between probability distributions in parameter space.

Treat the parameterized family as a Riemannian manifold and the Fisher information matrix as a Riemannian metric tensor.
• Proposed to use Fisher-Rao distance to measure the difference between two probability distributions.
• This paper is one of the earliest works to apply differential geometry methods to probabilistic models.

The content that needs to be rewritten is: Rao's photo with Cramér and Blackwell

In 1946, Rao went to Cambridge and became a disciple of Fisher. In 1948, under Fisher's guidance, he proposed the famous "

Score Test

(Score Test)".

Score test is one of the three major methods of statistical hypothesis testing

, which evaluates the constraints of statistical parameters based on the gradient of the likelihood function.

Compared with the Wald test and the likelihood ratio test, its main advantage lies in the convenience of calculation

For today's statistical practitioners, the score test can be said to be essential Basic statistical knowledge

Just this year, 102-year-old Professor Rao won the highest achievement award in statistics

International Prize in Statistics

(International Prize in Statistics).

The reason for the award is:

His work more than 70 years ago still has a profound impact on the scientific community.

His 1945 paper, published in the Bulletin of the Calcutta Mathematical Society, demonstrated three fundamental results that paved the way for modern statistics and provided statistical tools widely used in the scientific community today.

Professor Rao won many awards in his life and served as an academician of the Academy of Sciences in 8 countries including India, the United Kingdom, the United States and Italy

It is worth mentioning that he trained more than 50 doctors during his lifetime. Among them are Dabeeru C. Rao, director of the Department of Biostatistics at the University of Washington School of Medicine, Fellow of the American Statistical Association, and Indian statistician Debabrata Basu. They are all his students. When he was 100 years old, he did not Fully retired, still serving as professor emeritus at Pennsylvania State University and research professor at the University at Buffalo Modification

When the Indian media quoted his own statement, the last sentence became: "All methods of acquiring knowledge are essentially statistics."

All methods of acquiring knowledge are essentially statistics All can be summarized as statistics

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