Archive for Bruce Lindsay

estimating mixtures by polynomials

Posted in Books, Statistics, University life with tags , , , , , , , on April 7, 2016 by xi'an

mixture with unknown meansSida Wang, Arun Tejasvi, and Chaganty Percy Liang have just arXived a paper about using the method of moments to estimate mixtures of distributions. Method that was introduced (?) by Pearson in 1894 for a Gaussian mixture and crab data. And studied in fair details by Bruce Lindsay and his co-authors, including his book, which makes it the more surprising that Bruce’s work is not mentioned at all in the paper. In particular the 1989 Annals of Statistics paper which connects the number of components with the rank of a moment matrix in exponential family and which made a strong impression on me at the time, just when I was starting to work on mixtures. The current paper addresses more specifically the combinatoric difficulty of solving the moment equation. The solution proceeds via a relaxed convex optimisation problem involving a moment matrix, the relaxation removing the rank condition that identifies the parameters of the mixture. While I am no expert in the resolution of the associated eigenvalue problem (Algorithm 1), I wonder at (i) the existence and convergence of a solution when using empirical moments. And (ii) the impact of the choice of the moment equations, on both existence and efficiency of the moment method. It is clearly not invariant by reparameterisation, hence parameterisation matters. It is even unclear to me how many terms should be used in the resolution: if a single dimension is acceptable, determining this dimension may prove a complex issue.

Bruce Lindsay (March 7, 1947 — May 5, 2015)

Posted in Books, Running, Statistics, Travel, University life with tags , , , , , , , , , , , on May 22, 2015 by xi'an

When early registering for Seattle (JSM 2015) today, I discovered on the ASA webpage the very sad news that Bruce Lindsay had passed away on May 5.  While Bruce was not a very close friend, we had met and interacted enough times for me to feel quite strongly about his most untimely death. Bruce was indeed “Mister mixtures” in many ways and I have always admired the unusual and innovative ways he had found for analysing mixtures. Including algebraic ones through the rank of associated matrices. Which is why I first met him—besides a few words at the 1989 Gertrude Cox (first) scholarship race in Washington DC—at the workshop I organised with Gilles Celeux and Mike West in Aussois, French Alps, in 1995. After this meeting, we met twice in Edinburgh at ICMS workshops on mixtures, organised with Mike Titterington. I remember sitting next to Bruce at one workshop dinner (at Blonde) and him talking about his childhood in Oregon and his father being a journalist and how this induced him to become an academic. He also contributed a chapter on estimating the number of components [of a mixture] to the Wiley book we edited out of this workshop. Obviously, his work extended beyond mixtures to a general neo-Fisherian theory of likelihood inference. (Bruce was certainly not a Bayesian!) Last time, I met him, it was in Italia, at a likelihood workshop in Venezia, October 2012, mixing Bayesian nonparametrics, intractable likelihoods, and pseudo-likelihoods. He gave a survey talk about composite likelihood, telling me about his extended stay in Italy (Padua?) around that time… So, Bruce, I hope you are now running great marathons in a place so full of mixtures that you can always keep ahead of the pack! Fare well!