Stratified sampling and resampling for approximate Bayesian computation
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Approximate Bayesian computation (ABC) is computationally intensive for complex model simulators. To exploit expensive simulations, data-resampling was used with success in Everitt [2017] to obtain many artificial datasets at little cost and construct a synthetic likelihood. When using the same approach within ABC to produce a pseudo-marginal ABC-MCMC algorithm, the posterior variance is inflated, thus producing biased posterior inference. Here we use stratified Monte Carlo to considerably reduce the bias induced by data resampling. 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 resampled datasets, we obtain a less variable ABC likelihood and smaller integrated autocorrelation times. We consider simulation studies for static (Gaussian, g-and-k distribution, Ising model) and dynamic models (Lotka-Volterra).
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