Conditional particle filters (CPFs) with backward/ancestor sampling are powerful methods for sampling from the posterior distribution of the latent states of a dynamic model such as a hidden Markov model. However, the performance of these methods deteriorates with models involving weakly informative observations and/or slowly mixing dynamics. Both of these complications arise when sampling finely time-discretised continuous-time path integral models, but can occur with hidden Markov models too. Multinomial resampling, which is commonly employed with CPFs, resamples excessively for weakly informative observations and thereby introduces extra variance. Furthermore, slowly mixing dynamics render the backward/ancestor sampling steps ineffective, leading to degeneracy issues. We detail two conditional resampling strategies suitable for the weakly informative regime: the so-called `killing' resampling and the systematic resampling with mean partial order. To avoid the degeneracy issues, we introduce a generalisation of the CPF with backward sampling that involves auxiliary `bridging' CPF steps that are parameterised by a blocking sequence. We present practical tuning strategies for choosing an appropriate blocking. Our experiments demonstrate that the CPF with a suitable resampling and the developed `bridge backward sampling' can lead to substantial efficiency gains in the weakly informative and slow mixing regime.

翻译：条件后验粒子滤波（CPFs）结合回溯/祖先采样是从动态模型（如隐马尔可夫模型）潜在状态后验分布中采样的有效方法。然而，当模型涉及弱信息观测和/或慢混合动态时，这些方法的性能会下降。这两类复杂情况在采样精细时间离散化的连续时间路径积分模型时尤为常见，但也可能出现在隐马尔可夫模型中。CPF常用的多项式重采样在弱信息观测下会过度重采样，从而引入额外方差。此外，慢混合动态导致回溯/祖先采样步骤失效，引发退化问题。我们详细介绍了两种适用于弱信息场景的重采样策略：所谓的"消亡"重采样和基于均值偏序的系统重采样。为避免退化问题，我们提出了一种带有回溯采样的CPF的推广形式，该方法引入了由阻塞序列参数化的辅助"桥梁"CPF步骤。我们给出了选择合适阻塞参数的实际调优策略。实验表明，采用恰当重采样策略并配合所开发的"桥梁回溯采样"的CPF，在弱信息和慢混合条件下能显著提升效率。