We develop a computationally efficient framework for quasi-Bayesian inference based on linear moment conditions. The approach employs a delayed acceptance Markov chain Monte Carlo (DA-MCMC) algorithm that uses a surrogate target kernel and a proposal distribution derived from an approximate conditional posterior, thereby exploiting the structure of the quasi-likelihood. Two implementations are introduced. DA-MCMC-Exact fully incorporates prior information into the proposal distribution and maximizes per-iteration efficiency, whereas DA-MCMC-Approx omits the prior in the proposal to reduce matrix inversions, improving numerical stability and computational speed in higher dimensions. Simulation studies on heteroskedastic linear regressions show substantial gains over standard MCMC and conventional DA-MCMC baselines, measured by multivariate effective sample size per iteration and per second. The Approx variant yields the best overall throughput, while the Exact variant attains the highest per-iteration efficiency. Applications to two empirical instrumental variable regressions corroborate these findings: the Approx implementation scales to larger designs where other methods become impractical, while still delivering precise inference. Although developed for moment-based quasi-posteriors, the proposed approach also extends to risk-based quasi-Bayesian formulations when first-order conditions are linear and can be transformed analogously. Overall, the proposed algorithms provide a practical and robust tool for quasi-Bayesian analysis in statistical applications.

翻译：我们提出了一种计算高效的拟贝叶斯推断框架，该框架基于线性矩条件。该方法采用延迟接受马尔可夫链蒙特卡洛（DA-MCMC）算法，该算法使用代理目标核和从近似条件后验导出的提议分布，从而充分利用拟似然的结构。我们引入了两种实现方式：DA-MCMC-Exact将先验信息完全纳入提议分布，最大化每次迭代的效率；而DA-MCMC-Approx在提议分布中省略先验以减少矩阵求逆，从而提高高维情况下的数值稳定性和计算速度。对异方差线性回归的模拟研究表明，相较于标准MCMC和传统DA-MCMC基线方法，该方法在多元有效样本量（每迭代和每秒）方面取得了显著提升。Approx变体实现了最佳的整体吞吐量，而Exact变体则达到了最高的每次迭代效率。在两个实证工具变量回归中的应用进一步验证了这些发现：Approx实现能够扩展到更大规模的设计（其他方法在此情况下变得不切实际），同时仍能提供精确的推断。尽管该方法是为基于矩条件的拟后验而开发的，但当一阶条件为线性且可进行类似变换时，它也可扩展至基于风险的拟贝叶斯公式。总体而言，所提出的算法为统计应用中的拟贝叶斯分析提供了一种实用且稳健的工具。