Approximate Bayesian computation (ABC) is computationally intensive for complex model simulators. To exploit expensive simulations, data-resampling via bootstrapping can be employed to obtain many artificial datasets at little cost. However, when using this approach within ABC, the posterior variance is inflated, thus resulting in biased posterior inference. Here we use stratified Monte Carlo to considerably reduce the bias induced by data resampling. We also show empirically that it is possible to obtain reliable inference using a larger than usual ABC threshold. Finally, we show that with stratified Monte Carlo we obtain a less variable ABC likelihood. Ultimately we show how our approach improves the computational efficiency of the ABC samplers. We construct several ABC samplers employing our methodology, such as rejection and importance ABC samplers, and ABC-MCMC samplers. We consider simulation studies for static (Gaussian, g-and-k distribution, Ising model, astronomical model) and dynamic models (Lotka-Volterra). We compare against state-of-art sequential Monte Carlo ABC samplers, synthetic likelihoods, and likelihood-free Bayesian optimization. For a computationally expensive Lotka-Volterra case study, we found that our strategy leads to a more than 10-fold computational saving, compared to a sampler that does not use our novel approach.

翻译：Bayesian 附近的 Bayesian 计算(ABC ) 是在计算复杂的模型模拟器中密集的计算。 为了利用昂贵的模拟,可以通过靴子穿鞋进行数据取样,以低廉的成本获取许多人工数据集。 但是,在ABC内部使用这种方法时,后方差异会膨胀,从而产生偏颇的后方推论。 我们在这里使用分层的Monte Carlo, 以大量减少数据再抽样引出的偏差。 我们还从经验上表明,使用比通常的ABC阈值更大的ABC阈值获得可靠的样本推断是可能的。 最后,我们证明,通过分层的Monte Carlo,我们获得的ABC可能性较小。 我们最终展示了我们的方法如何提高ABC采样器的计算效率。 我们使用我们的方法,例如拒绝和重视ABC取样器,以及ABC-MC取样器。 我们考虑对静态的模拟研究(Gusian, g-k 和k 分布方式,Ising 模型,天文模型) 和动态模型(Lotka-Volterraralarala) 进行比我们州-Arestal 最廉价的BCreal Best 模型, 我们比较了一种比我们更自由的、更昂贵的Mestal Bestal- mactreal 的模型,我们找到一个比我们更有可能的AbCreal- mexbrasbrasbcrealbcreal 的模型,我们找到一个比较了一种比较了一种比较了一种比较了一种比较了一种比我们40的模型。