Debabrata Basu
Encyclopedia
Debabrata Basu (5 July 1924 – 24 March 2001) was a mathematical
statistician
who made fundamental contributions to the foundations
of statistics
. Basu invented simple examples that displayed some difficulties of likelihood
-based statistics and frequentist statistics; Basu's paradoxes were especially important in the development of survey sampling
. In statistical theory
, Basu's theorem
established
the independence
of a complete
sufficient statistic and an ancillary statistic
.
Born in Dacca, Bengal, in unpartitioned India (now in Bangladesh
), Basu was associated with the Indian Statistical Institute
in India
, and Florida State University
in the United States.
, unpartitioned India
, now Dhaka
, Bangladesh
. His father, N. M. Basu, was a mathematician specializing 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, Basu moved to Calcutta, where he worked for some time as an actuary
in an insurance company. In 1950, he joined the Indian Statistical Institute
as a research scholar under C.R. Rao.
In 1950, the Indian Statistical Institute was visited by Abraham Wald
, who was giving a lecture tour sponsored by the International Statistical Institute
. Wald greatly impressed Basu. Wald had developed a decision-theoretic foundations for statistics in which Bayesian statistics
was a central part, because of Wald's theorem characterizing admissible decision rule
s as Bayesian decision rules (or limits of Bayesian decision rules). Wald also showed the power of using measure-theoretic probability theory
in statistics.
After submitting in 1953 his thesis to the University of Calcutta
, Basu went as a Fullbright scholar to the University of California, Berkeley
. There Basu had intensive discussions with Jerzy Neyman
and "his brilliant younger colleagues" like Erich Leo Lehmann
. 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 A. Fisher
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 their festschrift for Basu, the editors M. Ghosh and Patak write that
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" and on the Fisher randomization test.
After teaching at the Indian Statistical Institute
Dr. Basu moved to the United States and taught statistics at Florida State University
from 1975 to 1990 when he was made an emeritus professor; he has supervised six students.
Mathematical statistics
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis...
statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
who made fundamental contributions to the foundations
Foundations of statistics
Foundations of statistics is the usual name for the epistemological debate in statistics over how one should conduct inductive inference from data...
of statistics
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
. Basu invented simple examples that displayed some difficulties of likelihood
Likelihood function
In statistics, a likelihood function is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values...
-based statistics and frequentist statistics; Basu's paradoxes were especially important in the development of survey sampling
Survey sampling
In statistics, survey sampling describes the process of selecting a sample of elements from a target population in order to conduct a survey.A survey may refer to many different types or techniques of observation, but in the context of survey sampling it most often involves a questionnaire used to...
. In statistical theory
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 statistical inference, and the actions and deductions that...
, Basu's theorem
Basu's theorem
In statistics, Basu's theorem states that any boundedly complete sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu....
established
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...
the independence
Statistical independence
In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs...
of a complete
Completeness (statistics)
In statistics, completeness is a property of a statistic in relation to a model for a set of observed data. In essence, it is a condition which ensures that the parameters of the probability distribution representing the model can all be estimated on the basis of the statistic: it ensures that the...
sufficient statistic and an ancillary statistic
Ancillary statistic
In statistics, an ancillary statistic is a statistic whose sampling distribution does not depend on which of the probability distributions among those being considered is the distribution of the statistical population from which the data were taken...
.
Born in Dacca, Bengal, in unpartitioned India (now in Bangladesh
Bangladesh
Bangladesh , officially the People's Republic of Bangladesh is a sovereign state located in South Asia. It is bordered by India on all sides except for a small border with Burma to the far southeast and by the Bay of Bengal to the south...
), Basu was associated with the Indian Statistical Institute
Indian Statistical Institute
Indian Statistical Institute is a public research institute and university in Kolkata's northern outskirt of Baranagar, India founded by Prasanta Chandra Mahalanobis in 1931...
in India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
, and Florida State University
Florida State University
The Florida State University is a space-grant and sea-grant public university located in Tallahassee, Florida, United States. It is a comprehensive doctoral research university with medical programs and significant research activity as determined by the Carnegie Foundation...
in the United States.
Biography
Debabrata Basu was born in Dacca, BengalBengal
Bengal is a historical and geographical region in the northeast region of the Indian Subcontinent at the apex of the Bay of Bengal. Today, it is mainly divided between the sovereign land of People's Republic of Bangladesh and the Indian state of West Bengal, although some regions of the previous...
, unpartitioned India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
, now Dhaka
Dhaka
Dhaka is the capital of Bangladesh and the principal city of Dhaka Division. Dhaka is a megacity and one of the major cities of South Asia. Located on the banks of the Buriganga River, Dhaka, along with its metropolitan area, had a population of over 15 million in 2010, making it the largest city...
, Bangladesh
Bangladesh
Bangladesh , officially the People's Republic of Bangladesh is a sovereign state located in South Asia. It is bordered by India on all sides except for a small border with Burma to the far southeast and by the Bay of Bengal to the south...
. His father, N. M. Basu, was a mathematician specializing 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, Basu moved to Calcutta, where he worked for some time as an actuary
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
in an insurance company. In 1950, he joined the Indian Statistical Institute
Indian Statistical Institute
Indian Statistical Institute is a public research institute and university in Kolkata's northern outskirt of Baranagar, India founded by Prasanta Chandra Mahalanobis in 1931...
as a research scholar under C.R. Rao.
In 1950, the Indian Statistical Institute was visited by Abraham Wald
Abraham Wald
- See also :* Sequential probability ratio test * Wald distribution* Wald–Wolfowitz runs test...
, who was giving a lecture tour sponsored by the International Statistical Institute
International Statistical Institute
The International Statistical Institute is a professional association of statisticians. The Institut International de Statistique or International Statistical Institute was founded in 1885 although there had been international congresses from 1853.. The Institute publishes a variety of books and...
. Wald greatly impressed Basu. Wald had developed a decision-theoretic foundations for statistics in which Bayesian statistics
Bayesian statistics
Bayesian statistics is that subset of the entire field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities...
was a central part, because of Wald's theorem characterizing admissible decision rule
Admissible decision rule
In statistical decision theory, an admissible decision rule is a rule for making a decision such that there isn't any other rule that is always "better" than it, in a specific sense defined below....
s as Bayesian decision rules (or limits of Bayesian decision rules). Wald also showed the power of using measure-theoretic probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
in statistics.
After submitting in 1953 his thesis to the University of Calcutta
University of Calcutta
The University of Calcutta is a public university located in the city of Kolkata , India, founded on 24 January 1857...
, Basu went as a Fullbright scholar to the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
. There Basu had intensive discussions with Jerzy Neyman
Jerzy Neyman
Jerzy Neyman , born Jerzy Spława-Neyman, was a Polish American mathematician and statistician who spent most of his professional career at the University of California, Berkeley.-Life and career:...
and "his brilliant younger colleagues" like Erich Leo Lehmann
Erich Leo Lehmann
Erich Leo Lehmann was an American statistician, who contributed to statistical and nonparametric hypothesis testing...
. Basu's theorem
Basu's theorem
In statistics, Basu's theorem states that any boundedly complete sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu....
comes from this time. Basu thus had a good understanding of the decision-theoretic approach to statistics of Neyman, Pearson
Egon Pearson
Egon Sharpe Pearson, CBE FRS was the only son of Karl Pearson, and like his father, a leading British statistician....
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 A. Fisher
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
in the winter of 1954–1955; he wrote in 1988, "With his reference set
Exact test
In statistics, an exact test is a test where all assumptions upon which the derivation of the distribution of the test statistic is based are met, as opposed to an approximate test, in which the approximation may be made as close as desired by making the sample size big enough...
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
Likelihood principle
In statistics,the likelihood principle is a controversial principle of statistical inference which asserts that all of the information in a sample is contained in the likelihood function....
". In their festschrift for Basu, the editors M. Ghosh and Patak write that
"[Basu's] critical 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" and on the Fisher randomization test.
After teaching at the Indian Statistical Institute
Indian Statistical Institute
Indian Statistical Institute is a public research institute and university in Kolkata's northern outskirt of Baranagar, India founded by Prasanta Chandra Mahalanobis in 1931...
Dr. Basu moved to the United States and taught statistics at Florida State University
Florida State University
The Florida State University is a space-grant and sea-grant public university located in Tallahassee, Florida, United States. It is a comprehensive doctoral research university with medical programs and significant research activity as determined by the Carnegie Foundation...
from 1975 to 1990 when he was made an emeritus professor; he has supervised six students.
External links
- Department of Statistics Florida State University
- Florida State Times Obituary
- Debabrata Basu: another photograph on the Portraits of Statisticians page.
- For Basu’s PhD students see
