Séminaire Parisien de statistique – October
To quote Valencia discussant favorite adjectives, the three talks were terrific and thought-provoking.
Eric Moulines presented Multiple Try Methods in MCMC algorithms. Instead of a unique proposal at each step, one proposes several values, among which only one is kept. The proposals can be chosen independant, but introducing dependence in the right way speeds up the rate of convergence to the stationary distribution. An interesting feature of this algorithm, espacially for Pierre, is that it allows parallel computation (in multiple propositions) whereas the standard Metropolis-Hastings algorithm is essentially sequential. See as well Pierre, Christian and Murray Smith’s block Independent Metropolis-Hastings algorithm for further details.
Jean-Marc Bardet introduced a way to detect ruptures in time series. He focuses on causal time series, ie they can be written only in terms of present and past innovations, for example . A rupture at time t means the parameters change at t.
The must-see talk for me was Eric Barat presentation on BNP modeling for sapce-time emission tomography. For new comer, BNP means more than a bank: Bayesian nonparametric. It is nice to see a very efficient application of BNP methods to a medical field. Eric kindly gives his slides (cf below) which I recommend, espacially the section on random probability measures: he reviews properties of the Dirichlet process, various representations (Chinese restaurant, Stick-breaking), and extends to the Pitman-Yor process and Pitman-Yor mixture. Then he gives posterior simulations by Gibbs sampling. I am interested in dependent over time models, and I am thankful for Eric for his pointer to a recent article of Chung and Dunson on local Dirichlet process, a nifty and simple construction of a Dependent Dirichlet process.
In a few days, I will try to make clear what the Dirichlet process is!