Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We consider an approach using a relatively large tolerance for the Markov chain Monte Carlo sampler to ensure its sufficient mixing, and post-processing the output leading to estimators for a range of finer tolerances. We introduce an approximate confidence interval for the related post-corrected estimators, and propose an adaptive approximate Bayesian computation Markov chain Monte Carlo, which finds a `balanced' tolerance level automatically, based on acceptance rate optimisation. Our experiments show that post-processing based estimators can perform better than direct Markov chain targetting a fine tolerance, that our confidence intervals are reliable, and that our adaptive algorithm leads to reliable inference with little user specification.

中文翻译：

---

关于使用近似贝叶斯计算马尔可夫链蒙特卡洛与膨胀容差和后校正

近似贝叶斯计算允许使用模型模拟推断具有难以处理的可能性的复杂概率模型。近似贝叶斯计算的马尔可夫链蒙特卡罗实现通常对容差参数敏感：低容差导致混合不良，大容差导致过度偏差。我们考虑了一种对马尔可夫链蒙特卡罗采样器使用相对较大容差的方法，以确保其充分混合，并对输出进行后处理，从而得出一系列更精细容差的估计器。我们为相关的后校正估计量引入了近似置信区间，并提出了自适应近似贝叶斯计算马尔可夫链蒙特卡罗，它基于接受率优化自动找到“平衡”容差水平。