We introduce two new classes of exact Markov chain Monte Carlo (MCMC) samplers for inference in latent dynamical models. The first one, which we coin auxiliary Kalman samplers, relies on finding a linear Gaussian state-space model approximation around the running trajectory corresponding to the state of the Markov chain. The second, that we name auxiliary particle Gibbs samplers corresponds to deriving good local proposals in an auxiliary Feynman--Kac model for use in particle Gibbs. Both samplers are controlled by augmenting the target distribution with auxiliary observations, resulting in an efficient Gibbs sampling routine. We discuss the relative statistical and computational performance of the samplers introduced, and show how to parallelise the auxiliary samplers along the time dimension. We illustrate the respective benefits and drawbacks of the resulting algorithms on classical examples from the particle filtering literature.

翻译：我们提出了两类新的精确马尔可夫链蒙特卡洛（MCMC）采样器，用于潜在动态模型中的推断。第一类采样器，我们称之为辅助卡尔曼采样器，其核心在于围绕马尔可夫链当前状态对应的游走轨迹，寻找一个线性高斯状态空间模型近似。第二类采样器，我们命名为辅助粒子吉布斯采样器，其方法是在辅助费曼-卡克模型中推导出适用于粒子吉布斯采样的优质局部提议分布。这两类采样器均通过向目标分布中添加辅助观测值进行控制，从而形成高效的吉布斯采样流程。我们讨论了所提出的采样器在统计与计算性能上的相对优劣，并展示了如何沿时间维度对辅助采样器进行并行化处理。最后，我们以粒子滤波文献中的经典案例，说明了所生成算法的各自优势与局限。