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Debabrata Basu (5 July 1924 – 24 March 2001) was an Indian statistician who made fundamental contributions to the
foundations of statistics The foundations of statistics concern the epistemological debate in statistics over how one should conduct inductive inference from data. Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist ...
. Basu invented simple examples that displayed some difficulties of
likelihood The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood functi ...
-based statistics and
frequentist statistics Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or pro ...
; Basu's paradoxes were especially important in the development of
survey sampling In statistics, survey sampling describes the process of selecting a sample of elements from a target population to conduct a survey. The term " survey" may refer to many different types or techniques of observation. In survey sampling it most ofte ...
. In
statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistica ...
, Basu's theorem established the
independence Independence is a condition of a person, nation, country, or state in which residents and population, or some portion thereof, exercise self-government, and usually sovereignty, over its territory. The opposite of independence is the st ...
of a complete
sufficient statistic In statistics, a statistic is ''sufficient'' with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the par ...
and an
ancillary statistic An ancillary statistic is a measure of a sample whose distribution (or whose pmf or pdf) does not depend on the parameters of the model. An ancillary statistic is a pivotal quantity that is also a statistic. Ancillary statistics can be used to co ...
. Page i in Basu was associated with the
Indian Statistical Institute Indian Statistical Institute (ISI) is a higher education and research institute which is recognized as an Institute of National Importance by the 1959 act of the Indian parliament. It grew out of the Statistical Laboratory set up by Prasanta ...
in India, and
Florida State University Florida State University (FSU) is a public research university in Tallahassee, Florida. It is a senior member of the State University System of Florida. Founded in 1851, it is located on the oldest continuous site of higher education in the sta ...
in the United States.Page i in "Preface" to IMS festschrift.


Biography

Debabrata Basu was born in
Dacca Dhaka ( or ; bn, ঢাকা, Ḍhākā, ), formerly known as Dacca, is the capital and largest city of Bangladesh, as well as the world's largest Bengali-speaking city. It is the eighth largest and sixth most densely populated city i ...
,
Bengal Bengal ( ; bn, বাংলা/বঙ্গ, translit=Bānglā/Bôngô, ) is a geopolitical, cultural and historical region in South Asia, specifically in the eastern part of the Indian subcontinent at the apex of the Bay of Bengal, predo ...
, unpartitioned
India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
, now
Dhaka Dhaka ( or ; bn, ঢাকা, Ḍhākā, ), formerly known as Dacca, is the capital and largest city of Bangladesh, as well as the world's largest Bengali-speaking city. It is the eighth largest and sixth most densely populated city ...
, Bangladesh. His father, N. M. Basu, was a mathematician specialising in number theory. Young Basu studied mathematics at Dacca University. He took a course in statistics as part of the under-graduate honours programme in Mathematics but his ambition was to become a pure mathematician. After getting his master's degree from Dacca University, Basu taught there from 1947 to 1948. Following the partition of India in 1947, Basu made several trips to India. In 1948, he moved to Calcutta, where he worked for some time as an
actuary An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset m ...
in an insurance company. In 1950, he joined the
Indian Statistical Institute Indian Statistical Institute (ISI) is a higher education and research institute which is recognized as an Institute of National Importance by the 1959 act of the Indian parliament. It grew out of the Statistical Laboratory set up by Prasanta ...
as a research scholar under C.R. Rao. In 1950, the Indian Statistical Institute was visited by
Abraham Wald Abraham Wald (; hu, Wald Ábrahám, yi, אברהם וואַלד;  – ) was a Jewish Hungarian mathematician who contributed to decision theory, geometry, and econometrics and founded the field of statistical sequential analysis. One of ...
, who was giving a lecture tour sponsored by the
International Statistical Institute The International Statistical Institute (ISI) is a professional association of statisticians. It was founded in 1885, although there had been international statistical congresses since 1853. The institute has about 4,000 elected members from gov ...
. Wald greatly impressed Basu. Wald had developed a decision-theoretic foundations for statistics in which
Bayesian statistics Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, ...
was a central part, because of Wald's theorem characterising
admissible decision rule In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always "better" than it (or at least sometimes better and never worse), in the precise sense of "better" define ...
s as Bayesian decision rules (or limits of Bayesian decision rules). Wald also showed the power of using measure-theoretic
probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...
in statistics. He married Kalyani Ray in 1952 and subsequently had two children, Monimala (Moni) Basu and Shantanu Basu. Moni is a journalism professor at the
University of Florida The University of Florida (Florida or UF) is a public land-grant research university in Gainesville, Florida. It is a senior member of the State University System of Florida, traces its origins to 1853, and has operated continuously on its Ga ...
and former
CNN CNN (Cable News Network) is a multinational cable news channel headquartered in Atlanta, Georgia, U.S. Founded in 1980 by American media proprietor Ted Turner and Reese Schonfeld as a 24-hour cable news channel, and presently owned by t ...
reporter, and Shantanu is an astrophysicist at the University of Western Ontario. In 1953, after submitting his thesis to the
University of Calcutta The University of Calcutta (informally known as Calcutta University; CU) is a public collegiate state university in India, located in Kolkata, West Bengal, India. Considered one of best state research university all over India every year, C ...
, Basu went as a
Fulbright scholar The Fulbright Program, including the Fulbright–Hays Program, is one of several United States Cultural Exchange Programs with the goal of improving intercultural relations, cultural diplomacy, and intercultural competence between the people of ...
to the
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant univ ...
. There Basu had intensive discussions with
Jerzy Neyman Jerzy Neyman (April 16, 1894 – August 5, 1981; born Jerzy Spława-Neyman; ) was a Polish mathematician and statistician who spent the first part of his professional career at various institutions in Warsaw, Poland and then at University College ...
and "his brilliant younger colleagues" like
Erich Leo Lehmann Erich Leo Lehmann (20 November 1917 – 12 September 2009) was a German-born American statistician, who made a major contribution to nonparametric hypothesis testing. He is one of the eponyms of the Lehmann–Scheffé theorem and of the Hodges� ...
. Basu's theorem comes from this time. Basu thus had a good understanding of the decision-theoretic approach to statistics of Neyman, Pearson and Wald. In fact, Basu is described as having returned from Berkeley to India as a "complete Neyman Pearsonian" by J. K. Ghosh. Basu met
Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who ...
in the winter of 1954–1955; he wrote in 1988, "With his reference set argument, Sir Ronald was trying to find a via media between the two poles of Statistics – Berkeley and Bayes. My efforts to understand this Fisher compromise led me to the
likelihood principle In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density ...
". In their
festschrift In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the ...
for Basu, the editors
Malay Ghosh Malay Ghosh ( Bengali: মলয় ঘোষ) is an Indian statistician and currently a Distinguished Professor at the University of Florida. He obtained a B.S. in 1962 from the University of Calcutta, and subsequently a M.A. in 1964 from the Un ...
and Patak write that
asu'scritical examination of both the Neyman–Pearsonian and the Fisherian modes of inference eventually forced him to a Bayesian point of view, via the likelihood route. The final conversion to Bayesianism came in January 1968, when Basu was invited to speak at a Bayesian Session in the Statistics Section of the Indian Science Congress. He confesses that, while preparing for these lectures, he became convinced that Bayesian inference did indeed provide one with a logical resolution of the underlying inconsistencies of both the Neyman–Pearson and the Fisherian theories. Since then, Dr. Basu became an ardent Bayesian and, in many of his foundation papers, pointed out the deficiencies of both the Neyman–Pearsonian and the Fisherian methods.
After 1968, Basu began writing polemical essays, which provided paradoxes to frequentist statistics, and which produced great discussion in statistical journals and at statistical meetings. Particularly stimulating papers were Basu's papers on the foundations of survey sampling. There is an extensive literature discussing Basu's problem of estimating the weight of the elephants at a circus with an enormous bull elephant named Jumbo, which Basu used to illustrate his objections to the
Horvitz–Thompson estimator In statistics, the Horvitz–Thompson estimator, named after Daniel G. Horvitz and Donovan J. Thompson, is a method for estimating the total and mean of a pseudo-population in a stratified sample. Inverse probability weighting is applied to ac ...
and to Fisher's randomisation test. Basu taught at the
Indian Statistical Institute Indian Statistical Institute (ISI) is a higher education and research institute which is recognized as an Institute of National Importance by the 1959 act of the Indian parliament. It grew out of the Statistical Laboratory set up by Prasanta ...
and various universities around the world. He moved to the United States and taught statistics at
Florida State University Florida State University (FSU) is a public research university in Tallahassee, Florida. It is a senior member of the State University System of Florida. Founded in 1851, it is located on the oldest continuous site of higher education in the sta ...
from 1975 to 1990 when he was made an emeritus professor; he has supervised six PhD students. In 1979 he was elected as a
Fellow of the American Statistical Association Like many other academic professional societies, the American Statistical Association (ASA) uses the title of Fellow of the American Statistical Association as its highest honorary grade of membership. The number of new fellows per year is limited ...
.View/Search Fellows of the ASA
, accessed 2016-08-20.


Publications

Basu's main articles are reprinted with his comments in Also


References


Further reading

*


External links


Department of Statistics Florida State UniversityDebabrata Basu: another photograph
on th

page. * For Basu's PhD students see {{DEFAULTSORT:Basu, Debabrata Survey methodologists Indian statisticians American statisticians 20th-century Indian mathematicians Bengali mathematicians Florida State University faculty 1924 births 2001 deaths People from Dhaka District University of Dhaka alumni University of Calcutta alumni University of Dhaka faculty Indian Statistical Institute alumni Indian Statistical Institute faculty Fellows of the American Statistical Association Scientists from Kolkata