Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) variants of approximate Bayesian computation are effective techniques for sampling posterior distributions in an approximate Bayesian computation. Since such approaches may result in biased inference or computationally inefficient sampling, rejection sampling for approximate Bayesian computation is found to be useful as it can result in independent, identically distributed samples from the approximated posterior. A method is developed for the acceleration of likelihood-free Bayesian inference that applies multilevel Monte Carlo (MLMC) variance reduction techniques directly to the rejection sampling. Application of the proposed MLMC ideas to the likelihood-free inference problem is demonstrated. Numerical results are provided to demonstrate the validity, accuracy and performance of the proposed method using some common models from epidemiology. The proposed method is found to retain accuracy advantages of rejection sampling while significantly improving the computational efficiency.
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机译：Markov Chain Monte Carlo（MCMC）和序贯蒙特卡罗（SMC）近似贝叶斯计算的变体是用于在近似贝叶斯计算中采样后分布的有效技术。由于这种方法可能导致偏置推断或计算效率低下的采样，因此发现用于近似贝叶斯计算的抑制采样是有用的，因为它可以从近似后的后部产生独立的，相同分布的样本。开发了一种用于加速无似然性贝叶斯推断的方法，该推论将多级蒙特卡罗（MLMC）方差减少技术直接应用于抑制采样。拟议的MLMC思想在似乎无似意推理问题的应用。提供了数值结果来展示使用来自流行病学的一些常见模型的所提出的方法的有效性，准确性和性能。发现所提出的方法可保持抑制采样的精度优势，同时显着提高计算效率。
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