Adaptive SMC

On Monday, Paul Fearnhead and Benjamin Taylor reposted on arXiv a paper about adaptive SMC. It is as well since I had missed the first posting on Friday. While the method has some similarities with our earlier work on population Monte Carlo methods with Olivier Cappé, Randal Douc, Arnaud Guillin and Jean-Michel Marin, there are quite novel and interesting features in this paper!  First, the paper is firmly set within a sequential setup, as in Chopin (2002, Biometrika) and Del Moral, Doucet and Jasra (2006, JRSS B). This means considering a sequence of targets corresponding to likelihoods with increasing datasets. We mentioned this case as a possible implementation of population Monte Carlo but never truly experimented with this. Fearnhead and Taylor do set their method within this framework, using a sequence of populations (or particle systems) aimed at this moving sequence of targets. The second major difference is that, while they also use a mixture of transition kernels as their proposal (or importance functions) and while they also aim at optimising the parameters of those transitions (parameters that I would like to dub cyberparameters to distinguish them from the parameters of the statistical model), they do not update those cyberparameters in a deterministic way, as we do. On the opposite, they build a non-parametric approximation to the distribution of those cyberparameters and simulate from those approximations at each step of the sequential algorithm, using a weight that assesses the quality of the move from to  , based on the simulated . I like very much this aspect of the paper, in that the cyberparameters are part of the dynamics in the stochastic algorithm, a point I tried to implement since the (never published) controlled MCMC paper with Christophe Andrieu. As we do in our paper now published in Statistics and Computing, they further establish that this method is asymptotically improving the efficiency criterion at each step of the sequential procedure. The paper concludes with an extensive simulation study where Fearnhead and Taylor show that their implementation outperforms random walk with adaptive steps. (I am not very happy with their mixture example in that they resort to an ordering on the means…)