State-space models (SSMs) are commonly used to model time series data where the observations depend on an unobserved latent process. However, inference on the model parameters of an SSM can be challenging, especially when the likelihood of the data given the parameters is not available in closed-form. One approach is to jointly sample the latent states and model parameters via Markov chain Monte Carlo (MCMC) and/or sequential Monte Carlo approximation. These methods can be inefficient, mixing poorly when there are many highly correlated latent states or parameters, or when there is a high rate of sample impoverishment in the sequential Monte Carlo approximations. We propose a novel block proposal distribution for Metropolis-within-Gibbs sampling on the joint latent state and parameter space. The proposal distribution is informed by a deterministic hidden Markov model (HMM), defined such that the usual theoretical guarantees of MCMC algorithms apply. We discuss how the HMMs are constructed, the generality of the approach arising from the tuning parameters, and how these tuning parameters can be chosen efficiently in practice. We demonstrate that the proposed algorithm using HMM approximations provides an efficient alternative method for fitting state-space models, even for those that exhibit near-chaotic behavior.

翻译：状态空间模型(SSMs)常用于对观测值依赖于不可观测潜变量过程的时间序列数据进行建模。然而，对SSM模型参数的推断可能具有挑战性，尤其是在给定参数下数据的似然函数无法以闭式表达时。一种方法是借助马尔可夫链蒙特卡洛(MCMC)和/或序贯蒙特卡洛近似方法联合采样潜状态与模型参数。当存在大量高度相关的潜状态或参数时，或当序贯蒙特卡洛近似中出现严重的样本贫化现象时，这些方法可能效率低下且混合性能较差。本文针对潜状态与参数联合空间的Metropolis-within-Gibbs采样提出了一种新颖的块状提议分布。该提议分布由确定性隐马尔可夫模型(HMM)引导，其定义方式保证了MCMC算法惯常的理论保障成立。我们探讨了HMM的构造方法、该方法的普适性（源自调优参数的选取）以及如何在实际中高效选择这些调优参数。实验证明，采用HMM近似所提出的算法为拟合状态空间模型（包括那些呈现近混沌行为的模型）提供了一种高效的替代方案。