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.

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