Semi-Complete Data Augmentation for Efficient State Space Model Fitting
提出一种结合数据增强与数值积分的贝叶斯混合算法，用于高效拟合状态空间模型，解决传统MCMC算法因状态与参数高度相关导致的低效问题，并在多个应用领域验证了其改善混合和降低自相关的效果。
We propose a novel efficient model-fitting algorithm for state space models. State space models are an intuitive and flexible class of models, frequently used due to the combination of their natural separation of the different mechanisms acting on the system of interest: the latent underlying system process; and the observation process. This flexibility, however, often comes at the price of more complicated modelfitting algorithms due to the associated analytically intractable likelihood. For the general case a Bayesian data augmentation approach is often employed, where the true unknown states are treated as auxiliary variables and imputed within the MCMC algorithm. However, standard "vanilla" MCMC algorithms may perform very poorly due to high correlation between the imputed states and/or parameters, often leading to model-specific bespoke algorithms being developed that are nontransferable to alternative models. The proposed method addresses the inefficiencies of traditional approaches by combining data augmentation with numerical integration in a Bayesian hybrid approach. This approach permits the use of standard "vanilla" updating algorithms that perform considerably better than the traditional approach in terms of improved mixing and lower autocorrelation, and has the potential to be incorporated into bespoke modelspecific algorithms. To demonstrate the ideas, we apply our semi-complete data augmentation algorithm to different application areas and models, leading to distinct implementation schemes and improved mixing and demonstrating improved mixing of the model parameters.