Abstract

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 model-fitting 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 model-specific 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. Supplementary materials for this article are available online.

摘要

我们提出了一种用于状态空间模型的新型高效模型拟合算法。状态空间模型是一类直观且灵活的模型，由于它们对作用于感兴趣系统的不同机制的自然分离的组合而经常使用：潜在的底层系统过程；和观察过程。然而，由于相关的难以分析的可能性，这种灵活性通常是以更复杂的模型拟合算法为代价的。对于一般情况，通常采用贝叶斯数据增强方法，其中真实的未知状态被视为辅助变量并在 MCMC 算法中估算。然而，由于估算状态和/或参数之间的高度相关性，标准的“香草”MCMC 算法可能表现非常差，通常会导致开发特定于模型的定制算法，这些算法不可转移到替代模型。所提出的方法通过将数据增强与贝叶斯混合方法中的数值积分相结合来解决传统方法的低效率问题。这种方法允许使用标准的“香草”更新算法，这些算法在改进混合和降低自相关方面比传统方法表现得更好，并且有可能被纳入定制的模型特定算法中。为了展示这些想法，我们将我们的半完整数据增强算法应用于不同的应用领域和模型，从而导致不同的实施方案和改进的混合，并展示了模型参数的改进混合。本文的补充材料可在线获取。