Anil Kumar Bhattacharyya

Anil Kumar Bhattacharyya (Bengali: অনিল কুমার ভট্টাচার্য) (1 April 1915 – 17 July 1996) was an Indian statistician who worked at the Indian Statistical Institute in the 1930s and early 40s. He made fundamental contributions to multivariate statistics, particularly for his measure of similarity between two multinomial distributions, known as the Bhattacharyya coefficient, based on which he defined a metric, the Bhattacharyya distance. This measure is widely used in comparing statistical samples in biology, physics, computer science, etc.

Anil Kumar Bhattacharyya
Born(1915-04-01)1 April 1915
Bhatpara, Kolkata Bengal Presidency, British India (Now West Bengal, India)
Died17 July 1996(1996-07-17) (aged 81)
CitizenshipIndia
Alma materRajabazar Science College
(University of Calcutta)
Known forBhattacharyya distance, Bhattacharyya bound
Scientific career
FieldsStatistician
InstitutionsUniversity of Calcutta, Indian Statistical Institute

Distance between statistical distributions had been addressed in 1936 by Mahalanobis, who proposed the D2 metric, now known as Mahalanobis distance. Subsequently, Bhattacharyya defined a cosine metric for distance between distributions, in a Calcutta Mathematical Society paper in 1943,[1][2] expanding on some of the results in another paper in Sankhya in 1946.[3] Bhattacharyya's two major research concerns were the measurement of divergence between two probability distributions and the setting of lower bounds to the variance of an unbiased estimator.

Life

Bhattacharyya was born to Bhavanath and Lilavati, sometime in March–April 1915 (in the month Chaitra Bengali: চৈত্র of the year 1321, the exact date is not known)[4] at Bhatpara in the district of 24 Parganas of West Bengal. He passed the Matriculation Examination of Calcutta University in 1932 and I. Sc. Examination in 1934 from Hooghly Mohsin College. In 1936 he ranked first in the First Class at the B.A./B.Sc. examination from the same college and went over to the renowned Science College, Calcutta University for an M.Sc. in Mathematics. Here he had F. W. Levi and Raj Chandra Bose as his teachers and passed the M.A. Examination in 1938 with the first rank in the First Class.

In 1939, at Levi's suggestion, Bhattacharyya met P. C. Mahalanobis and joined Indian Statistical Institute as an honorary worker.[5] In 1941, he was made a part-time lecturer in the newly formed Statistics Department of Calcutta University, headed by Mahalanobis. Here he had C. R. Rao, H. K. Nandi and T. P. Choudhury, as his students. He went to Patna to take up the job of Statistical Officer of Bihar Government, in December 1943 and, in 1946, he returned to Calcutta to join Indian Statistical Institute as Superintending Statistician (in charge of training). Mahalanobis requested him to concurrently take classes in the Statistics Department of Presidency College. After the post was created, Bhattacharyya was made a whole-time Senior Professor and Head of the Department in 1949. He occupied the post of Senior Professor until his retirement in March 1974, but in 1967 he stepped down from the leadership, apparently piqued by certain moves of the West Bengal Government's Education Department.[4] Almost since his retirement from Government service, he had been associated with the Narendrapur Ramakrishna Mission Residential College as a guest teacher, where a Memorial Scholarship is awarded in his name.[6]

Works
  • "A note on Ramamurti's problem of maximal sets", Sankhya, 6 (1942) 189 - 192. [7]
  • "On a measure of divergence between two statistical populations defined by their probability distributions", Bull. Cal. Math. Soc, 35 (1943) 99 - 109. [2]
  • "On some sets of sufficient conditions leading to the normal bivariate distribution", Sankhya, 6 (1943) 399 - 406. [8]
  • "On some analogues of the amount of information and their uses in statistical estimation" I, Sankhya, 8 (1946) 1 - 14. [10]
  • "On some analogues of the amount of information and their uses in statistical estimation" II, Sankhya, 8 (1947) 201 - 218. [11]
  • "On some analogues of the amount of information and their uses in statistical estimation" III, Sankhya, 8 (1948) 315 - 328. [12]
  • "On a measure of divergence between two multinomial populations", Sankhya, 7 (1946), 401 - 406. [3]
  • "Unbiased statistics with minimum variance", Proc. Roy. Soc. Edin., A, 63 (1950), 69 - 77. [13]
  • "The theory of regression in statistical population admitting local parameters", Bull. Int. Stat. Inst., 33, Part II (1951).
  • "On some uses of the t-distribution in multivariate analysis", Sankhya, 12 (1952), 89 - 104. [14]
  • "Notes on the use of unbiased and biased statistics in the binomial population", Cal. Stat. Assoc. Bull., 5 (1954), 149 - 164.
  • "Some uses of the 'amount of information' in the statistical inference", (address of the Sectional President), Proc. Ind. Sc. Cong., 46th Session (1959). [15]
  • "On a geometrical representation of probability distribution and its use in statistical inference", Cal. Stat. Assoc. Bull., 40 (1990–91), 23 - 49. [16]

References
  1. Bhattacharyya, A. (1943). "On a measure of divergence between two statistical populations defined by their probability distributions". Calcutta Mathematical Society. 35: 99–109. MR 0010358.
  2. "Bulletin of the Calcutta Mathematical Society, Vol-35". 1943. Article: "On a measure of divergence between two statistical populations defined by their probability distributions" is in Page: 99-109 {{cite journal}}: Cite journal requires |journal= (help)
  3. Bhattacharyya, A. (1946). "On a Measure of Divergence between Two Multinomial Populations". Sankhyā. 7 (4): 401–406. JSTOR 25047882.
  4. S. P. Mukherjee; Arijit Chaudhuri; Sujit K. Basu (1994). A. M. Gun on behalf of the Organizing Committee, Golden Jubilee Celebrations (ed.). Essays on probability and statistics: Festschrift in honour of Professor Anil Kumar Bhattacharyya. Department of Statistics, Presidency College.
  5. C R Rao, Prasantha Chandra Mahalanobis (1893-1972), Biographical Memoirs of Fellows of the Royal Society, v.19 (Dec 1973), pp.455-492
  6. "www.rkmcnarendrapur.org/index1.php?page=scholarship/". Rkmcnarendrapur.org. Archived from the original on 14 January 2018. Retrieved 25 February 2013.
  7. Bhattacharyya, A. (1942). "A Note on Ramamurti's Problem of Maximal Sets". Sankhyā. 6 (2): 189–192. JSTOR 25047757.
  8. Bhattacharyya, A. (1943). "On Some Sets of Sufficient Conditions Leading to the Normal Bivariate Distribution". Sankhyā. 6 (4): 399–406. JSTOR 25047806.
  9. Bhattacharyya, A. (1945). "A Note on the Distribution of the Sum of Chi-Squares". Sankhyā. 7 (1): 27–28. JSTOR 25047828.
  10. Bhattacharyya, A. (1946). "On Some Analogues of the Amount of Information and Their Use in Statistical Estimation". Sankhyā. 8 (1): 1–14. JSTOR 25047921.
  11. Bhattacharyya, A. (1947). "On Some Analogues of the Amount of Information and Their Use in Statistical Estimation (Contd.)". Sankhyā. 8 (3): 201–218. JSTOR 25047948.
  12. Bhattacharyya, A. (1948). "On Some Analogues of the Amount of Information and Their Use in Statistical Estimation (Concluded)". Sankhyā. 8 (4): 315–328. JSTOR 25047897.
  13. Bhattacharyya, A. (1950). "Unbiased Statistics with Minimum Variance". Proceedings of the Royal Society of Edinburgh. Section A: Mathematics. 63 (1): 69–77. doi:10.1017/S0080454100006993. S2CID 124275255.
  14. Bhattacharyya, A. (1952). "On the Uses of the t-Distribution in Multivariate Analysis". Sankhyā. 12 (1/2): 89–104. JSTOR 25048117.
  15. "Forty Sixth Indian Science Congress Proceedings of the Statistics Section". Calcutta Statistical Association Bulletin. 9 (1–2): 29–45. 1959. doi:10.1177/0008068319590103. S2CID 220749750. Summary of Prof. A Bhattacharyya's presidential address at the Statistics Section of the Indian Science Congress Association Meeting in Delhi, 1959
  16. Bhattacharyya, A. (1990). "On a Geometrical Representation of Probability Distributions and its use in Statistical Inference". Calcutta Statistical Association Bulletin. 40 (1–4): 23–49. doi:10.1177/0008068319900504. S2CID 125793582.
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