J.K. Ghosh in 2010, during a trip to the Lake of Ozarks, MO. Photo: Jyotishka Datta

Professor Jayanta K. Ghosh passed away on September 30; he was 80. J.K. Ghosh was born in Calcutta, India, on May 23, 1937. Over a period of nearly 60 years, Professor Ghosh made timely and insightful contributions to a wide swath of theoretical statistics. Sanghamitra Bandyopadhyay, the Director of the Indian Statistical Institute (ISI) said, “Through the process of asking and settling many important questions, and mentoring of our students, Professor Ghosh was, and remains, an inspiration. He commanded the respect of students, scientists and workers of the ISI for his formidable scholarship and exemplary kindness.”

Ghosh’s earliest work was influenced by Abraham Wald’s invention of the SPRT. As a twenty-something, in 1960, he studied the ASN and the efficiency of the sequential t-test, as a part of his Calcutta University PhD dissertation under the supervision of H.K. Nandi. A few years later, simultaneously and independently, with Jack Hall and Bob Wijsman, he wrote a fundamental paper formalizing the results of Charles Stein and Don Burkholder on commutativity of reduction by invariance and sufficiency. This work was later followed up by others, and was cited in Ferguson’s classic text.

Around this time, C.R. Rao was publishing his path-breaking results on second order efficiency of the MLE among asymptotically normal first order efficient estimates. Around 1970, Ghosh, jointly with his student Kasala Subrahmanyam, began his long journey into higher order asymptotics, and in well known later work with many others, established second order risk optimality of the MLE under essentially all bounded convex loss functions. It was evident that Ghosh admired MLEs (and perhaps LRT). He saw MLEs as more-or-less Bayesian objects. In his discussion of Brad Efron’s 1975 curvature paper, Ghosh shows open disdain for frequentist statistics, likening it to Lewis Carroll’s Cheshire cat, all but dead save its ironic grin. It is not clear if he was already a committed Bayesian at that point, although he was obviously supportive of Basu’s epic articles on likelihood and information, and edited a Springer monograph compiling Basu’s main work at that point.

Professor Ghosh’s most cited work is his 1978 joint paper with Rabi Bhattacharya on the validity of Edgeworth expansions for smooth functionals in the iid or independent situations. The work is widely regarded as a masterpiece in controlling the error in the central limit theorem. Earlier, Professor Ghosh had given a very sweet alternative proof of Bahadur’s classic stochastic representation of quantiles as asymptotically linear statistics, under one less derivative than Jack Kiefer would need, but with an in probability remainder, unlike Kiefer. For many first order results, this suffices.

In the mid-80s, Ghosh became the Director of the Indian Statistical Institute (ISI). His tenure was marked by prudence and negotiation. As the ISI directorship was coming to an end, he was hired as a visiting professor at Purdue University in 1990, and tenured in 1997. On his arrival there, he converted his NSF-CBMS lectures into the well known IMS monograph on higher order asymptotics. At this time, he became the President of the International Statistical Institute.

Professor Ghosh also showed his first interests in Bayesian model selection at that time by revisiting Schwarz’s work. The interest later blossomed into full fledged work with Jim Berger and numerous other collaborators. Undoubtedly, he helped popularize and sometimes clarify fractional Bayes factors, and objective priors custom-made for model selection. He provided clarifications and publicity for Bernardo priors, and in a long series of papers with many coauthors established Bayesian (hierarchical) resolutions of various types of Neyman–Scott quagmires. Many of these things, along with modern Bayesian computing, found their way into his Springer text on Bayesian analysis written with Mohan Delampady and Tapas Samanta.

Although for a large part of his career he concentrated on parametric models, one of his prime contributions to Bayesian statistics is the fundamental Springer book with R.V. Ramamoorthi on Bayesian nonparametrics. Later, jointly with Aad van der Vaart and his students Subhashis Ghoshal and R.V. Ramamoorthi, he wrote two major papers on consistency of Ferguson mixtures. Ghosh presented a part of this research at the International Congress of Mathematicians.

Although a theoretician, Ghosh had an interest in modeling and looking at data. He used to regularly collaborate with Bijoy Singha Mazumder and Supriya Sengupta on sediment transportation and grain size distributions. At the inspiration of Vijay Nair, jointly with Pulakesh Maiti, T.J. Rao and Bikas Sinha, he wrote a historical article on statistics in India. He was visibly proud of the heritage of the ISI, and often mentioned in conversation students and colleagues there.

In the post Rao–Basu era, Professor Ghosh acted as a unique coalescing force for Indian statistics within India, and served as a bridge between Indian statistics and statistics in the west. Two important examples are his organizing roles in the 1974 conference at the ISI in Calcutta on Recent Trends in Statistics, and the 1980 conference at the ISI in Delhi in honor of C.R. Rao’s sixtieth birthday.

Over a period of 35 years, Professor Ghosh received numerous awards. He was awarded the Bhatnagar prize by the CSIR of India in 1981, the Presidency of the statistics section of the Indian Science Congress in 1991, the Mahalanobis gold medal of the Indian Science Congress in 1998, the P.V. Sukhatme prize in statistics of the Government of India in 2000, an honorary D.Sc. degree by the B.C. Roy Agricultural University in West Bengal, India in 2006, the Lifetime Achievement award of the International Indian Statistical Association in 2010, an honorary D.Sc. degree by the ISI in 2012, and the Padma Shree award of the Government of India in 2014. He was also a Fellow of the National Academy of Science of India and the IMS.

Ghosh was a private person, but maintained committed friendships with many people. He was well read in both Indian and western literature and was fond of Tagore’s poetic songs. He was spectacularly devoted to his family and was an exemplary father and husband (his wife, Ira, passed away a few weeks before him). In a clearly distinguished career, Professor Ghosh influenced the work of various spectra of statisticians at different times, was an undisputed leader of Indian statistics, and produced an enviable number of successful students. It is an extraordinary legacy.

Written by Anirban DasGupta, Purdue University