Conditional particle filters with bridge backward sampling

The performance of the conditional particle filter (CPF) with backward sampling is often impressive even with long data records. However, when the observations are weakly informative relative to the dynamic model, standard multinomial resampling is wasteful and backward sampling has limited effect. In particular, with time-discretised continuous-time path integral models, backward sampling degenerates in refined discretisations. 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 issue of backward sampling, we introduce a generalisation that involves backward sampling with an auxiliary `bridging' CPF step, which is 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 regime.