C Radhakrishna Rao, a trailblazer in the field of Statistics, passed away on August 23. Rao, who was a respected professor at Pennsylvania State University, was 102 years old.
- At the age of 24 in 1945, Rao gained recognition for his groundbreaking paper in the Bulletin of the Calcutta Mathematical Society.
- He was affiliated with the Indian Statistical Institute when he wrote this revolutionary paper.
- His work addressed three fundamental problems and had a wide-ranging impact on many scientific fields such as social sciences, engineering, and biology.
Rao made several important contributions in his career. However, three key achievements outlined in his 1945 paper stand out:
- The creation of the Cramér-Rao lower bound.
- The development of the Rao-Blackwell Theorem.
- The inception of a new area called “information geometry”.
In April 2023, he received the prestigious International Prize in Statistics, and these three remarkable achievements were prominently featured in the official announcement.
Key Points Of Rao’s Theorems
In the field of statistics, making estimates and drawing inferences from collected data is a common task. Two significant results from Rao’s work in 1945, namely the Cramér-Rao lower bound and the Rao-Blackwell Theorem, are closely related to the quality of these inferences.
- Rao developed two significant results in 1945 – the Cramér-Rao lower bound and the Rao-Blackwell Theorem. These help statisticians make better inferences from collected data.
- The Cramér-Rao lower bound provides a measure of the accuracy of an estimate.
- On the other hand, the Rao-Blackwell Theorem offers a method to enhance an estimate optimally.
- Harold Cramér and David Blackwell were the mathematicians who independently established these results, hence the names of the theorems.
- Interestingly, Rao was unaware of these scientists’ works when he developed his theorem.
- Rao’s journey to these discoveries began in 1944 when he taught about the Fisher Information, a method used for large data samples.
- A question from a student regarding the application of Fisher Information for smaller samples led Rao to work out his famous results applicable to any sample size, all in a day.
The Impact
- The Cramér-Rao lower bound is a tool used across many areas where data analysis is crucial.
- Some of its key applications include signal processing, spectroscopy, and radar systems.
- It’s also utilized in multiple-image radiography, risk evaluation, and quantum physics.
- On the other hand, the Rao-Blackwell theorem also finds wide-ranging use.
- It’s implemented in fields like stereology and particle filtering.
- Additionally, it’s crucial in computational econometrics.
- The importance of these tools is highlighted by the International Prize in Statistics Foundation.
- Rao’s research connected probability models to differential geometry, a field that uses algebra and calculus for studying shapes and spaces.
- Differential geometry uses algebra and calculus to explore specific shapes and spaces. This influential work led to a third renowned result.
- The study helped establish ‘information geometry’, a discipline that applies differential geometry principles to probability theory.
- Information geometry is a tool that has been employed in several scientific areas. For instance, it has aided in understanding the measurements of the Higgs boson at the Large Hadron Collider.
- It has also been utilised in recent research related to radars and antennas, and it has contributed to advancements in artificial intelligence and signal processing.
- Signal processing is a domain that involves analyzing different types of signals. These signals could be sound, images, or potential fields.
- Critical methodologies in signal processing, such as the Cramér-Rao lower bound and information geometry, are widely used.
C Radhakrishna Rao’s Legacy
- Krishna Rao’s work has left a significant mark in various fields, especially in statistics. Here are some key points about his contributions:
- Rao’s work is so influential that many technical terms bear his name. These terms, including the Cramér-Rao lower bound, Rao-Blackwell Theorem, Fisher-Rao Theorem, Rao Distance, and Rao’s Orthogonal Arrays, are found in numerous statistics textbooks.
- Rao has received numerous prestigious awards for his work. In India, he was honoured with the Padma Bhushan (1968) and the Padma Vibhushan (2001), the Shanti Swarup Bhatnagar Award (1963), and the India Science Award (2009).
- Internationally, he received the US National Medal of Science (2002) and the International Prize in Statistics.
- To honor Rao’s impact, the Indian government established a biennial award in statistics named ‘The Professor C R Rao’ Award.
- The CR Rao Advanced Institute of Mathematics, Statistics and Computer Science and Prof. C R Rao Road in Hyderabad were named in his honor.
- Pennsylvania State University also established the C R and Bhargavi Rao Prize in Statistics.
- Rao’s work has been fundamental in econometrics. He developed methods that improved the reliability of population-wide data estimates. These methods significantly influence current research and policymaking globally.
- In the early years of India’s independence, Rao advocated for increased data collection and established research units within government departments. His advocacy marked the beginning of data-informed policymaking in India.