Conditional particle filters with bridge backward sampling

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.