Jayanta Kumar Ghosh [1937-2017]

Just head from Sonia and Judith that our friend and fellow Bayesian Jayanta K Ghosh (জয়ন্ত কুমার ঘোষ in Bengali) has passed away a few days ago in Lafayette. He was a wonderful man, very kind to everyone and open for discussing all aspects of Bayesian theory and methodology. While he worked on many branches of statistics, he is more know to Bayesians for his contributions to Bayesian asymptotics. From Bernstein-von-Mises convergence theorems to frequentist validation of non-informative priors, to the Bayesian analysis of infinite dimensional problems, including consistency of posteriors and rates of convergence, and to Bayesian and Empirical Bayes model selection rules in high dimensional problems. He also wrote an introductory textbook on Bayesian Statistics ten years ago with Mohan Delampady and Tapas Samanta. And a monograph of higher order asymptotics. I knew from this summer that J K was quite sick and am quite sad to learn of his demise. He will be missed by all for his gentleness and by Bayesians for his contributions to the fields of objective and non-parametric Bayesian statistics…

Stochastic approximation in mixtures

On Friday, a 2008 paper on Stochastic Approximation and Newton’s Estimate of a Mixing Distribution by Ryan Martin and J.K. Ghosh was posted on arXiv. (I do not really see why it took so long to post on arXiv a 2008 Statistical Science paper but given that it is not available on project Euclid, it may be that not all papers in Statistical Science are published immediately. Anyway, this is irrelevant to my point here!).

The paper provides a very nice introduction to stochastic approximation methods, making the link to recent works by Christophe Andrieu, Heikki Haario, Faming Liang, Eric Moulines, Enro Saksman, and co-authors. Martin and Ghosh also reinterpret Newton-Raphson as a special case of stochastic approximation. The whole paper is very pleasant to read, quite in tune with Statistical Science. I will most certainly use this material in my graduate courses and also include part of it in the revision of Monte Carlo Statistical Methods.