CSMC with Optional Resampling

[THargreaves]

The definitions of CSMC that I can find seem to assume that resampling takes place at every step and so don't worry about setting the weight for the reference trajectory.

We need to think carefully about what this weight should be.

[charlesknipp]

I personally don't see any problems with resampling at every step. Although, Chopin's implementation of CSMC sets ESSmin = 0.5 by default (see here). I'm not too experienced with Particle Gibbs in practice, so I don't have a tough stance on this either way.

[THargreaves]

Ah okay, so he must show how to handle the weights in the case of no resampling somewhere in the code base then. Struggling to find where though

Oh wait it's literally in the code snippet you shared. He just sets the value and doesn't update the weight. That feels a bit strange to me

[charlesknipp]

The CSMC class he defines only overloads generate_particles and resample_move, so the reweight_particles function is still performed at every iteration of the filter. For reference, his generic SMC code is linked here

[THargreaves]

Generalising this issue to talk about all issues related to the implementation details of CSMC.

Our previous approach was saving the filtered states but this doesn't work for Rao-Blackwellisation if we're going to "insert" the reference trajectory at the end of the predict step. In this case the Gaussian state is essentially corrected twice leading to the wrong estimates.

I've done a temporary fix by saving the proposed states but I think the better idea would be to save the filtered states and update the ref after the update step.

[THargreaves]

The CSMC class he defines only overloads generate_particles and resample_move, so the reweight_particles function is still performed at every iteration of the filter. For reference, his generic SMC code is linked here

What I mean is that during generate_particles he just overwrites the first value of X but doesn't touch the log weights. I'm assuming this must be correct but it's surprising to me in the optional resampling case.

[THargreaves]

Relevant: https://stats.stackexchange.com/questions/351249/importance-weight-of-conditioned-particle-in-conditional-smc