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Implement CSMC in cuthbert#181

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Implement CSMC in cuthbert#181
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csmc

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@AdrienCorenflos
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@AdrienCorenflos AdrienCorenflos linked an issue Feb 8, 2026 that may be closed by this pull request
@AdrienCorenflos
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I'm a little unclear whether the paradigm is reasonable: in some sense, CSMC is not really a time-step level routine, so doing a filter_combine style stuff may not be the best
The question is: I'm quite clear we shouldn't give the MCMC loop, but what is the level at which we are working? Full fwd/bwd passes, or one step of each and then somehow call filter/smoother on them?

@SamDuffield
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So good to get started on Markov kernels!

We can definitely discuss a unified API for this mcmc folder which I think can/should be different to the existing cuthbert/inference.py to reflect the different nature of operations (Markovian, inherently offline).

Another point is the nature of model_inputs. So far cuthbert doesn’t assume any structure (aside from a temporal axis where appropriate) leaving it purely as user defined data for the model rather than anything specific for the inference method. I think we should continue that. Here it might make sense to have a prev_trajectory argument or similar with the reference particle etc.

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Implement conditional SMC

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