Sequential Bayesian Predictive Synthesis

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.