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

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.

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 the distance between multinomial distributions, this work despite being submitted for publication in 1941, appeared almost five years later in Sankhya.[1][2] Progress toward more general results, which defines the distance metric between two probability distributions which are absolutely continuous with respect to the Lebesgue measure, has been done by Bhattacharyya, which has come in 1942, at Proceedings of the Indian Science Congress.[3] The final work towards this direction appeared in 1943, in the Bulletin of the Calcutta Mathematical Society.[4]

Bhattacharyya's other research concerns were characterization of classical bivariate normal distribution through normal conditional distributions[5] 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)[6] at Bhatpara in the district of 24 Parganas of West Bengal. His birth name was Anilkumar Bhattacharyya (does not have any middle name, his entire first name was Anilkumar, thus in all of his works his name appeared as A. Bhattacharyya). 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.[7] 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.[6] 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.[8] In 1994, on the occasion of its golden jubilee celebration Department of Statistics, Presidency University (then Presidency College), released a Festschrift in honour of Professor Bhattacharyya.[6]

Works

  • "A note on Ramamurti's problem of maximal sets", Sankhya, 6 (1942) 189 - 192.[9]
  • "On discrimination and divergence", Proc. Ind. Sc. Cong., 29th Session (1942).[3][10]
  • "On a measure of divergence between two statistical populations defined by their probability distributions", Bull. Cal. Math. Soc, 35 (1943) 99 - 109.[4]
  • "On some sets of sufficient conditions leading to the normal bivariate distribution", Sankhya, 6 (1943) 399 - 406.[11]
  • "On a measure of divergence between two multinomial populations", Sankhya, 7 (1946), 401 - 406.[1]
  • "On some analogues of the amount of information and their uses in statistical estimation" I, Sankhya, 8 (1946) 1 - 14.[13]
  • "On some analogues of the amount of information and their uses in statistical estimation" II, Sankhya, 8 (1947) 201 - 218.[14]
  • "On some analogues of the amount of information and their uses in statistical estimation" III, Sankhya, 8 (1948) 315 - 328.[15]
  • "Unbiased statistics with minimum variance", Proc. Roy. Soc. Edin., A, 63 (1950), 69 - 77.[16]
  • "The problem of regression in statistical population admitting local parameters", Bull. Int. Stat. Inst., 33, Part II (1951), 29 - 54.[17]
  • "Some uses of the t-statistic in multivariate analysis", Proc. Ind. Sc. Cong., 38th Session (1951).
  • "On some uses of the t-distribution in multivariate analysis", Sankhya, 12 (1952), 89 - 104.[18]
  • "Notes on the use of unbiased and biased statistics in the binomial population", Cal. Stat. Assoc. Bull., 5 (1954), 149 - 164.[19]
  • "Some uses of the 'amount of information' in the statistical inference", (address of the Sectional President), Proc. Ind. Sc. Cong., 46th Session (1959).[20] An abridged form of the aforementioned presidential address (statistical section) is also available and appeared in the Calcutta Statistical Association Bulletin.[21]
  • "On a geometrical representation of probability distribution and its use in statistical inference", Cal. Stat. Assoc. Bull., 40 (1990–91), 23 - 49.[22]

References

  1. 1 2 Bhattacharyya, A. (1946). "On a Measure of Divergence between Two Multinomial Populations". Sankhyā. 7 (4): 401–406. JSTOR 25047882. MR 0018387.
  2. ↑ Sen, Pranab Kumar (1996). "Anil Kumar Bhattacharyya (1915-1996): A Reverent Remembrance". Calcutta Statistical Association Bulletin. 46 (3–4): 151–158. doi:10.1177/0008068319960301. ISSN 0008-0683. S2CID 164326977.
  3. 1 2 Indian Science Congress (1942). Proceedings Of The Twenty-ninth Indian Science Congress (1942). The Indian Science Congress Association, Calcutta.
  4. 1 2 Bhattacharyya, A (1943). "On a measure of divergence between two statistical populations defined by their probability distributions". Bulletin of the Calcutta Mathematical Society. 35: 99–109. MR 0010358. S2CID 235941388. The article: "On a measure of divergence between two statistical populations defined by their probability distributions" is on Pages: 99-109
  5. ↑ Arnold, Barry C. (1999). "Variations on a Bhattacharyya Theme". Calcutta Statistical Association Bulletin. 49 (1–2): 23–30. doi:10.1177/0008068319990102. ISSN 0008-0683. MR 1744884. S2CID 125755221.
  6. 1 2 3 Mukherjee, S. P.; Chaudhuri, Arijit; Basu, Sujit K., eds. (1994). Essays on probability and statistics: Festschrift in honour of Professor Anil Kumar Bhattacharyya. A.M. Gun on behalf of the Organising Committee, Golden Jubilee Celebrations, Dept. of Statistics, Presidency College, Calcutta, Calcutta, 1994. OCLC 230185222.
  7. ↑ C R Rao, Prasantha Chandra Mahalanobis (1893-1972), Biographical Memoirs of Fellows of the Royal Society, v.19 (Dec 1973), pp.455-492
  8. ↑ "www.rkmcnarendrapur.org/index1.php?page=scholarship/". Rkmcnarendrapur.org. Archived from the original on 14 January 2018. Retrieved 25 February 2013.
  9. ↑ Bhattacharyya, A. (1942). "A Note on Ramamurti's Problem of Maximal Sets". Sankhyā. 6 (2): 189–192. JSTOR 25047757. MR 0008326.
  10. ↑ "Indian Statistical Institute: Eleventh Annual Report: 1942-43". Sankhyā: The Indian Journal of Statistics (1933-1960). 6 (4): 431–441. 1943. ISSN 0036-4452. Page 10 of this supporting document shows that a paper on divergence named 'On discrimination and divergence' was submitted to the proceedings of the Indian Science Congress.
  11. ↑ Bhattacharyya, A. (1943). "On Some Sets of Sufficient Conditions Leading to the Normal Bivariate Distribution". Sankhyā. 6 (4): 399–406. JSTOR 25047806. MR 0010360.
  12. ↑ Bhattacharyya, A. (1945). "A Note on the Distribution of the Sum of Chi-Squares". Sankhyā. 7 (1): 27–28. JSTOR 25047828. MR 0013271.
  13. ↑ Bhattacharyya, A. (1946). "On Some Analogues of the Amount of Information and Their Use in Statistical Estimation". Sankhyā. 8 (1): 1–14. JSTOR 25047921. MR 0020242.
  14. ↑ 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. MR 0023503.
  15. ↑ 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. MR 0026302.
  16. ↑ 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. MR 0035947. S2CID 124275255.
  17. ↑ Bhattacharyya, A (1951). "The problem of regression in statistical population admitting local parameters". Bulletin of the International Statistical Institute. 33: 29–54. MR 0069464.
  18. ↑ Bhattacharyya, A. (1952). "On the Uses of the t-Distribution in Multivariate Analysis". Sankhyā. 12 (1/2): 89–104. JSTOR 25048117. MR 0058921.
  19. ↑ Bhattacharyya, A (1954). "Notes on the use of unbiased and biased statistics in the binomial population". Calcutta Statistical Association Bulletin. 5: 149–164. MR 0067422.
  20. ↑ Indian Science Congress (1959). INDIAN SCIENCE CONGRESS ASSOCIATION PART-2. INDIAN SCIENCE CONGRESS ASSOCIATION,CALCUTTA.
  21. ↑ "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
  22. ↑ 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. MR 1172634. S2CID 125793582.
  1. ↑ Mukherjee, S. P.; Chaudhuri, Arijit; Basu, Sujit K., eds. (1994). Essays on probability and statistics: Festschrift in honour of Professor Anil Kumar Bhattacharyya. A.M. Gun on behalf of the Organising Committee, Golden Jubilee Celebrations, Dept. of Statistics, Presidency College, Calcutta, Calcutta, 1994. OCLC 230185222.
  2. ↑ Gupta, S. Das (1995). "Review of Essays on Probability and Statistics: Festschrift in Honour of Professor Anil Kumar Bhattacharyya". Sankhyā: The Indian Journal of Statistics, Series A (1961-2002). 57 (1): 166–166. ISSN 0581-572X.
  3. ↑ "Review of Essays on Probability and Statistics: Festschrift in Honour of Professor Anil Kumar Bhattacharyya". Biometrics. 52 (3): 1163–1163. 1996. doi:10.2307/2533086. ISSN 0006-341X.
  4. ↑ Senroy, Sugata (1995). "Book Review". Calcutta Statistical Association Bulletin. 45 (1–2): 131–136. doi:10.1177/0008068319950110. ISSN 0008-0683.
  5. ↑ Rbl (1997). "Review of Essays on Probability and Statistics. Festschrift in Honour of Professor Anil Kumar Bhattacharyya". Journal of the American Statistical Association. 92 (437): 390–390. doi:10.2307/2291500. ISSN 0162-1459.
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