Research seminar by Prof. T. E. S. Raghavan

Posted on January 22, 2026 by administrator

IM K hosted its seventh research seminar on January 08, 2026, for the year 2025-26. It was conducted by Prof. T. E. S. Raghavan, emeritus professor at the University of Illinois, Chicago, USA.

The topic was On the applications of scaling the entries of a matrix

Abstract of the talk given below

Various biological, statistical, and social science data come in the form of cross-classified counts tables commonly known as contingency tables. Scaling the cell entries of such multidimensional matrices involves both mathematically and statistically well-posed problems of practical interest. In this talk, we first describe several situations where scaling can be useful.

We also describe a natural scaling algorithm in the problem of scaling a nonnegative matrix to obtain the prescribed row and column sums. we consider the problem of maximum likelihood estimation in contingency tables.

This area of statistics, which forms part of discrete multivariate analysis, is of considerable interest to researchers at present. We will motivate this topic of scaling with examples chosen from 1. Budget allocations 2. Infra structure planning, 3. Gaussian elimination and problems of accuracy. 4. Arriving at approximate maximum likelihood estimates in say a 2 by 2 by 2 contingency table.

Without any proof at the very end we will just mention a   general existence  theorem which subsumes all such problems.  We also propose several intuitive algorithms to handle some of these problems.