Dynamic Bayesian predictive synthesis is a formal approach to coherently synthesizing multiple predictive distributions into a single distribution. In sequential analysis, the computation of the synthesized predictive distribution has heavily relied on the repeated use of the Markov chain Monte Carlo method. The sequential Monte Carlo method in this problem has also been studied but is limited to a subclass of linear synthesis with weight constraint but no intercept. In this study, we provide a custom, Rao-Blackwellized particle filter for the linear and Gaussian synthesis, supplemented by timely interventions by the MCMC method to avoid the problem of particle degeneracy. In an example of predicting US inflation rate, where a sudden burst is observed in 2020-2022, we confirm the slow adaptation of the predictive distribution. To overcome this problem, we propose the estimation/averaging of parameters called discount factors based on the power-discounted likelihoods, which becomes feasible due to the fast computation by the proposed method.

翻译：动态贝叶斯预测综合是一种将多个预测分布一致性地综合为单一分布的形式化方法。在序贯分析中，综合预测分布的计算高度依赖于马尔可夫链蒙特卡洛方法的反复使用。该问题中的序贯蒙特卡洛方法虽已有研究，但仅限于不含截距项且带有权重约束的线性综合子类。本研究针对线性高斯综合场景，提出了一种定制的 Rao-Blackwellized 粒子滤波器，并辅以马尔可夫链蒙特卡洛方法的适时干预，以避免粒子退化问题。在预测2020-2022年间观测到突发性飙升的美国通胀率的实例中，我们确认了预测分布存在适应性滞后的现象。为解决该问题，我们提出基于幂折扣似然估计/平均折扣因子参数的方法——由于所提方法的高速计算能力，这一方法得以实现。