标题： 回归调整近似贝叶斯计算的收敛性 显示英文标题

标题： Convergence of Regression Adjusted Approximate Bayesian Computation

摘要： 我们给出了Beaumont(2002)提出的近似贝叶斯计算回归调整版本的渐近结果。 我们证明了对于合适的带宽选择，回归调整将导致后验分布，在渐近意义下能够正确量化不确定性。 此外，对于这样的带宽选择，我们可以实现一个重要抽样算法来从后验分布中抽样，其接受概率随着数据样本量的增加趋于1。 这与标准近似贝叶斯计算的结果形成有利对比，在标准近似贝叶斯计算中，唯一能获得正确量化不确定性的后验分布的方法是选择一个小得多的带宽；这种带宽的接受概率趋于零，因此蒙特卡洛误差将占主导地位。 显示英文摘要

摘要： We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior that, asymptotically, correctly quantifies uncertainty. Furthermore, for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data sample size increases. This compares favourably to results for standard approximate Bayesian computation, where the only way to obtain a posterior that correctly quantifies uncertainty is to choose a much smaller bandwidth; one for which the acceptance probability tends to zero and hence for which Monte Carlo error will dominate.