## SMC²

Posted in Statistics, University life with tags , , , , on March 11, 2011 by xi'an

Pierre Jacob, along with Nicolas Chopin and Omiros Papaspiliopoulos, completed a massive work on SMC², a sequential Monte Carlo method that builds on the particle MCMC discussion paper of Andrieu, Doucet and Hollenstein. The major advance is to incorporate sequential requirements within the pMCMC scheme for processing state space models,

$y_t|x_{1:t},y_{1:(t-1)},\theta \sim f(y_t|x_t,\theta) \quad x_t|x_{1:(t-1)}\sim q(x_t|x_{t-1},\theta)$

while still estimating the parameters of the model. A preliminary version was put on arXiv in January, but they reworked their examples towards more realistic and complex cases. One of the new examples is an exciting problem about women’s records on 3000m with an incredible gain of 16 seconds in 1993.

Pierre gave us a presentation at CREST last morning, whose slides are available on slideshare. (The beginning is a standard reminder on sequential Monte Carlo in state-space/hidden Markov models. A question that popped out during the talk is whether or not the estimator of the marginal likelihood derived from the weights of the sequential methods was trustworthy. The error rate is in O(T).) I recall that pMCMC (discussed in this post) is a regular (valid) MCMC algorithm that involves a SMC at each iteration leading to use the approximation of the marginal likelihood $p(y_{1:T}|\theta)$ within the Metropolis-Hastings acceptance ratio. SMC² stands for “SMC on SMC” and it indeed uses a sequential particle approximation to run the pMCMC on a sequential basis. The paper establishes the validity of the scheme via a (huge) completion argument. The examples provided therein are quite complex hidden Markov models and the performances of the SMC² fairly convincing.

## Seminar im Heidelberg

Posted in Books, pictures, Running, Statistics, Travel with tags , , , , on April 18, 2010 by xi'an

Even though I can report only today for unexpected family issues (and not at all for the Icelandic volcano ashes!), I have had a wonderful trip to Heidelberg! Both seminars were packed with students, many more than faculty, I met a PhD student working on ABC who travelled all the way from Bonn to attend the seminars and discuss with me, I had highly informative statistics discussions with the local faculty (about ABC, point processes, particle filters, graphical models, stochastic volatility, covariance estimation, and more), plus great runs, up the local hills, a few glimpses of the old city, and good local beer and food! Had the internet connection worked (better), I would have been a bit more efficient, but this led me to take the philosophy way for a few days. and progress in my evaliation of Evidence and Evolution. Thanks to Tilmann Gneiting for the invitation and for the warm welcome!