## the ABC-SubSim algorithm

**I**n a nice coincidence with my ABC tutorial at AISTATS 2014 – MLSS, Manuel Chiachioa, James Beck, Juan Chiachioa, and Guillermo Rus arXived today a paper on a new ABC algorithm, called ABC-SubSim. The *SubSim* stands for subset simulation and corresponds to an approach developed by one of the authors for rare-event simulation. This approach looks somewhat similar to the cross-entropy method of Rubinstein and Kroese, in that successive tail sets are created towards reaching a very low probability tail set. Simulating from the current subset increases the probability to reach the following and less probable tail set. The extension to the ABC setting is done by looking at the acceptance region (in the augmented space) as a tail set and by defining a sequence of tolerances. The paper could also be connected with nested sampling in that constrained simulation through MCMC occurs there as well. Following the earlier paper, the MCMC implementation therein is a random-walk-within-Gibbs algorithm. This is somewhat the central point in that the sample from the previous tolerance level is used to start a Markov chain aiming at the next tolerance level. (Del Moral, Doucet and Jasra use instead a particle filter, which could easily be adapted to the modified Metropolis move considered in the paper.) The core difficulty with this approach, not covered in the paper, is that the MCMC chains used to produce samples from the constrained sets have to be stopped at some point, esp. since the authors run those chains in parallel. The stopping rule is not provided (see, e.g., Algorithm 3) but its impact on the resulting estimate of the tail probability could be far from negligible… Esp. because there is no burnin/warmup. (I cannot see how “ABC-SubSim exhibits the benefits of perfect sampling” as claimed by the authors, p. 6!) The authors re-examined the MA(2) toy benchmark we had used in our earlier survey, reproducing as well the graphical representation on the simplex as shown above.

November 4, 2014 at 5:45 pm

Subset Simulation (and thus ABC-SubSim) indeed exhibits the benefits of ‘prefect sampling’: If you look at how the intermediate levels are defined, you will realize that the samples used as MCMC seeds are actually samples from the target distribution. Consequently, no burn-in is required.