Lieu : IHP, Amphithéâtre Hermite.
14.00 : Sylvain LE CORFF (Université Paris-Sud Orsay)
Titre : Oscillation Processes and Phase Estimation in Nonlinear State Space Models
Résumé : In this talk, we consider a new model for time series with a specific oscillation pattern. The generalized state space model we introduce is given by a hidden stochastic phase process only observed through an unknown periodic function f characterizing the pattern. The identifiability of the model is established under mild assumptions on the pattern f. Then, a new method for statistical inference based on Sequential Monte Carlo methods (in this case a particle smoother) and a nonparametric Expectation Maximization algorithm is developed. The case of time-varying amplitude
and baseline is also introduced. In this context, a Rao-Blackwellized particle smoother that combines a Kalman smoother and an efficient sequential Monte Carlo smoother is suggested. The performance of the method for practical applications is demonstrated through simulations and an application to human electrocardiogram recordings.
15.00 : Nicolas CHOPIN (ENSAE)
Titre : Sequential Quasi-Monte Carlo, application to filtering, smoothing, and other statistical problems (joint work with Mathieu Gerber, Harvard University)
Résumé : We derive and study SQMC (Sequential Quasi-Monte Carlo), a class of algorithms obtained by introducing QMC point sets in particle filtering. The complexity of SQMC is O(NlogN), where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate OP(N-1/2). The only requirement to implement SQMC is the ability to write the simulation of particle xnt given xnt-1 as a deterministic function of xnt-1 and a fixed number of uniform variates. We show that SQMC is amenable to the same extensions as standard SMC, such as forward smoothing, backward smoothing, unbiased likelihood evaluation, and so on. In particular, SQMC may replace SMC within a PMCMC (particle Markov chain Monte Carlo) algorithm. We establish several convergence results. We provide numerical evidence that SQMC may significantly outperform SMC in practical scenarios.
16.00 : Pierre LATOUCHE (Université Paris 1 Panthéon-Sorbonne)
Titre : Goodness of fit of logistic models for random graphs
Résumé : We consider binary networks along with covariate information on the edges. In order to take these covariates into account, logistic-type models for random graphs are often considered. One of the main questions which arises in practice is to assess the goodness of fit of a model. To address this problem, we add a general term, related to the graphon function of W-graph models, to the logistic models. Such an extra term can be approximated from a blockwise constant function obtained using stochastic block models with increasing number of clusters. If the given network is fully explained by the covariates, then a sole block should be estimated from data. This framework allows to derive a testing procedure from a model based selection context. Bayes factors or posterior odds can then be used for decision making. Overall, the logistic model considered necessitates two types of variational approximations to derive the model selection approach.