He works in the fields of probability theory and theoretical statistics where he has made fundamental contributions to long-standing problems in both areas.

Most notable are (1) his solution to the multidimensional rate of convergence problem for the central limit theorem in his Ph.D. thesis[1] published in the Bulletin of the American Mathematical Society[2] and further elaborated in a research monograph[3] written jointly with R. Ranga Rao and (2) the solution of the validity of the formal Edgeworth expansion in collaboration with J.K. Ghosh in 1978.

[4] He has also contributed significantly to the theory and application of Markov processes, including numerous co-authored papers on problems in groundwater hydrology with Vijay K. Gupta, and in economics with Mukul Majumdar.

Bhattacharya was born January 11, 1937, in his ancestral home Porgola, Barisal District, in the present country of Bangladesh.

In 1988, he and M. Denker were invited by the German Mathematical Society to give DMV Seminar, Band 14, published by Birkhäuser as ″Asymptotic Statistics″.