Interweaving Markov Chain Monte Carlo Strategies for Efficient Estimation of Dynamic Linear Models

In dynamic linear models (DLMs) with unknown fixed parameters, a standard Markov chain Monte Carlo (MCMC) sampling strategy is to alternate sampling of latent states conditional on fixed parameters and sampling of fixed parameters conditional on latent states. In some regions of the parameter space, this standard data augmentation (DA) algorithm can be inefficient. To improve efficiency, we apply the interweaving strategies of Yu and Meng to DLMs. For this, we introduce three novel alternative DAs for DLMs: the scaled errors, wrongly scaled errors, and wrongly scaled disturbances. With the latent states and the less well known scaled disturbances, this yields five unique DAs to employ in MCMC algorithms. Each DA implies a unique MCMC sampling strategy and they can be combined into interweaving and alternating strategies that improve MCMC efficiency. We assess these strategies using the local level model and demonstrate that several strategies improve efficiency relative to the standard approach and the most efficient strategy interweaves the scaled errors and scaled disturbances. Supplementary materials are available online for this article.