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：本文提出了一种基于线性矩条件的计算高效拟贝叶斯推断框架。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源自近似条件后验的提议分布，从而充分利用拟似然的结构。我们介绍了两种实现方案：DA-MCMC-Exact将先验信息完全纳入提议分布以最大化单次迭代效率，而DA-MCMC-Approx则在提议分布中省略先验以减少矩阵求逆运算，从而在更高维度下提升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（按迭代次数和秒数计算）指标上均取得显著提升。Approx变体实现了最佳整体吞吐量，而Exact变体则达到最高的单次迭代效率。在两个实证工具变量回归中的应用验证了这些发现：Approx实现能够扩展到更大规模的设计问题（此时其他方法已不适用），同时仍能提供精确推断。虽然本方法是为基于矩条件的拟后验分布而设计，但当一阶条件为线性且可进行类似变换时，该方法也可扩展至基于风险的拟贝叶斯框架。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实用且稳健的工具。