Approximate Bayesian computation (ABC) is a class of Bayesian inference algorithms that targets for problems with intractable or {unavailable} likelihood function. It uses synthetic data drawn from the simulation model to approximate the posterior distribution. However, ABC is computationally intensive for complex models in which simulating synthetic data is very expensive. In this article, we propose an early rejection Markov chain Monte Carlo (ejMCMC) sampler based on Gaussian processes to accelerate inference speed. We early reject samples in the first stage of the kernel using a discrepancy model, in which the discrepancy between the simulated and observed data is modeled by Gaussian process (GP). Hence, the synthetic data is generated only if the parameter space is worth exploring. We demonstrate from theory, simulation experiments, and real data analysis that the new algorithm significantly improves inference efficiency compared to existing early-rejection MCMC algorithms. In addition, we employ our proposed method within an ABC sequential Monte Carlo (SMC) sampler. In our numerical experiments, we use examples of ordinary differential equations, stochastic differential equations, and delay differential equations to demonstrate the effectiveness of the proposed algorithm. We develop an R package that is available at https://github.com/caofff/ejMCMC.

翻译：近似贝叶斯计算（ABC）是一类针对似然函数难以处理或不可用问题的贝叶斯推断算法，通过从仿真模型中抽取合成数据来近似后验分布。然而，对于合成数据模拟成本高昂的复杂模型，ABC的计算强度极大。本文提出一种基于高斯过程的早期拒绝马尔可夫链蒙特卡洛（ejMCMC）采样器，用于加速推断速度。我们利用差异模型——即采用高斯过程（GP）对模拟数据与观测数据之间的差异进行建模——在核的第一阶段即早期拒绝样本。因此，仅当参数空间值得探索时才生成合成数据。我们从理论、仿真实验和真实数据分析中证明，与现有早期拒绝MCMC算法相比，新算法显著提升了推断效率。此外，我们将所提方法应用于ABC序贯蒙特卡洛（SMC）采样器。在数值实验中，我们通过常微分方程、随机微分方程和延迟微分方程实例验证了所提算法的有效性。我们开发了R程序包，可从https://github.com/caofff/ejMCMC获取。