While Bayesian inference has become increasingly popular with advances in computational resources, its algorithms can be computationally prohibitive and may not scale with large datasets. This has led to growing interest in alternative algorithms, such as approximation methods and variants of Markov chain Monte Carlo. Among these approaches, prior proposal-recursive Bayesian (PP-RB) inference facilitates scalable Bayesian computation by recursively updating the posterior distribution across stages and utilizing parallel computing resources. While the well-known ``degeneracy'' issue in PP-RB has been studied, another limitation that PP-RB can yield incorrect inferences when posterior distributions shift substantially between stages has remained unsolved. To address this, we propose parallel-tempered prior proposal-recursive Bayesian (PPP-RB) inference, which extends PP-RB by leveraging the key idea underlying Metropolis-coupled Markov chain Monte Carlo. We show both theoretically and empirically that PPP-RB targets the true posterior distribution. We illustrate PPP-RB through numerical studies and real data analysis in application to earthquake count data and sea surface salinity in the North Atlantic region. In these applications, we compare PPP-RB with PP-RB and a standard MCMC, demonstrating that PPP-RB is more efficient in terms of effective sample size per elapsed time.

翻译：尽管随着计算资源的进步，贝叶斯推理日益普及，但其算法在计算上可能成本高昂，且难以随大数据集扩展。这引发了对替代算法的兴趣，例如近似方法和马尔可夫链蒙特卡洛（MCMC）的变体。在这些方法中，先验提议-递归贝叶斯（PP-RB）推理通过跨阶段递归更新后验分布并利用并行计算资源，实现了可扩展的贝叶斯计算。虽然PP-RB中著名的“退化”问题已得到研究，但另一个局限——当后验分布在阶段间显著变化时，PP-RB可能得出错误推理——仍未解决。为解决此问题，我们提出了并行回火先验提议-递归贝叶斯（PPP-RB）推理，它通过利用Metropolis耦合马尔可夫链蒙特卡洛的核心思想扩展了PP-RB。我们从理论和经验两方面证明，PPP-RB能够针对真实后验分布。我们通过数值研究和实际数据分析（应用于地震计数数据和北大西洋区域的海表盐度）来说明PPP-RB。在这些应用中，我们将PPP-RB与PP-RB及标准MCMC进行比较，表明PPP-RB在单位时间的有效样本量方面更为高效。