# Umberto Picchini: Stratified sampling and bootstrapping for approximate Bayesian computation

Umberto Picchini (Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SWE) will give a talk on October 15th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.

Umberto Picchini is Associate Professor at the Chalmers University of Technology and University of Gothenburg (SWE)

**Title:** Stratified sampling and bootstrapping for approximate Bayesian computation

**Abstract: **Approximate Bayesian computation (ABC) is the most popular methodology for likelihood-free inference. Its main feature is the ability to bypass the explicit calculation of the likelihood function, by only requiring access to a model simulator to generate many artificial datasets. However, ABC is computationally intensive for complex model simulators. To exploit expensive simulations, nonparametric bootstrapping was used with success in [1] to obtain many artificial datasets at little cost and construct a "synthetic likelihood" (another likelihood-free procedure). When using the same approach within ABC to produce a pseudo-marginal ABC-MCMC algorithm, the posterior variance results inflated, thus producing biased posterior inference. Here we construct approximations of the ABC likelihood using stratified Monte Carlo, to considerably reduce the bias induced by bootstrapping. We show that it is possible to obtain reliable inference using a larger than usual ABC threshold, by employing stratified Monte Carlo. Finally, we show that by averaging over multiple bootstrapped datasets, we obtain a less variable ABC likelihood and smaller integrated autocorrelation times.

[joint work with Richard Everitt]

[1] Everitt (2017). Bootstrapped synthetic likelihood. arXiv preprint arXiv:1711.05825.

Download the flyer here.