A state-space model is a time-series model that has an unobserved latent process from which we take noisy measurements over time. The observations are conditionally independent given the latent process and the latent process itself is Markovian. These properties lead to simplifications for the conditional distribution of the latent process given the parameters and the observations. This chapter looks at how we can leverage the properties of state-space models to construct efficient MCMC samplers. We consider a range of Gibbs-sampler schemes, including those which use the forward-backward algorithm to simulate from the full conditional of the latent process given the parameters. For models where the forward-backward algorithm is not applicable we look at particle MCMC algorithms that, given the parameters, use particle filters to approximately simulate from the latent process or estimate the likelihood of the observations. Throughout, we provide intuition and informally discuss theory about the properties of the model that impact the efficiency of the different algorithms and how approaches such as reparameterization can improve mixing.

翻译：状态空间模型是一种时间序列模型，其包含一个不可观测的潜在过程，我们随时间对该过程进行带噪声的测量。在给定潜在过程的条件下，观测值条件独立，且潜在过程本身具有马尔可夫性。这些特性使得在给定参数和观测值的条件下，潜在过程的条件分布得以简化。本章探讨如何利用状态空间模型的特性来构建高效的MCMC采样器。我们考虑了一系列吉布斯采样方案，包括使用前向-后向算法从给定参数条件下潜在过程的完全条件分布中进行采样的方案。对于前向-后向算法不适用的模型，我们研究了粒子MCMC算法，这些算法在给定参数条件下，使用粒子滤波器近似地从潜在过程采样或估计观测值的似然。自始至终，我们提供直观解释并非正式地讨论了影响不同算法效率的模型特性相关理论，以及诸如重参数化等方法如何改善混合性能。