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与行列式，通常计算成本高昂。DA-MCMC通过两阶段过程应对这一挑战：第一阶段使用近似后验筛选提议值，第二阶段基于精确目标后验做出最终接受或拒绝决策。这减少了昂贵矩阵运算的需求，从而在不牺牲精度的前提下提升效率。我们通过合成数据与真实数据的应用验证了DA-MCMC的有效性。结果表明，尽管DA-MCMC每迭代的有效样本量略低于标准MCMC，但其在每秒有效样本量方面实现约两倍的效率提升。这使得DA-MCMC特别适用于后验模拟计算量大的场景。因此，DA-MCMC算法为拟贝叶斯推断的计算效率带来显著进展，成为稳健贝叶斯分析的重要工具。