This study introduces a computationally efficient algorithm, delayed acceptance Markov chain Monte Carlo (DA-MCMC), designed to improve posterior simulation in quasi-Bayesian inference. Quasi-Bayesian methods, which do not require fully specifying a probabilistic model, are often computationally expensive owing to the need to evaluate the inverse and determinant of large covariance matrices. DA-MCMC addresses this challenge by employing a two-stage process: In the first stage, proposals are screened using an approximate posterior, whereas a final acceptance or rejection decision is made in the second stage based on the exact target posterior. This reduces the need for costly matrix computations, thereby improving efficiency without sacrificing accuracy. We demonstrate the effectiveness of DA-MCMC through applications to both synthetic and real data. The results demonstrate that, although DA-MCMC slightly reduces the effective sample size per iteration compared with the standard MCMC, it achieves substantial improvement in terms of effective sample size per second, approximately doubling the efficiency. This makes DA-MCMC particularly useful for cases where posterior simulation is computationally intensive. Thus, the DA-MCMC algorithm offers a significant advancement in computational efficiency for quasi-Bayesian inference, making it a valuable tool for robust Bayesian analysis.

翻译：本研究提出了一种计算高效的算法——延迟接受马尔可夫链蒙特卡洛（DA-MCMC），旨在改进拟贝叶斯推断中的后验模拟。拟贝叶斯方法无需完全指定概率模型，但由于需要计算大型协方差矩阵的逆矩阵和行列式，通常计算成本高昂。DA-MCMC通过采用两阶段流程应对这一挑战：第一阶段使用近似后验对提议进行筛选，而第二阶段则基于精确目标后验做出最终的接受或拒绝决策。这减少了对昂贵矩阵计算的需求，从而在不牺牲准确性的前提下提高了效率。我们通过合成数据和实际数据的应用验证了DA-MCMC的有效性。结果表明，虽然与标准MCMC相比，DA-MCMC每次迭代的有效样本量略有减少，但以每秒有效样本量衡量的效率实现了显著提升，约提高了一倍。这使得DA-MCMC在后验模拟计算密集的场景中尤为有用。因此，DA-MCMC算法为拟贝叶斯推断的计算效率带来了重要进展，成为鲁棒贝叶斯分析的有力工具。