Improve (hopefully) how HybridGibbs uses samplers state and history

[nabriis]

Closes #483.

This PR makes it such that HybridGibbs will extract each of its samplers state and history, then reinitialize the sampler with a new target, then set the sampler state and history from earlier.

This reason we have to do this is because changing .target will not always correctly set all internal variables of the samplers that depend on the target.

Also thanks to Silja, ensured that acc rate is stored correctly in HybridGibbs.

Suggestion for review if method works

Use CWMH and compare with HybridGibbs using MH. Are the results similar? Test both warmup and sampling.

Silja reviewed and tested. Result OK.

[siljachr]

The MH sampler did not append to self._acc, and therefore self._acc stayed at the initial value 1, which meant that the tune method increased the step length to the maximum (i.e. 1). I have pushed a small change that fixes this.

In line 220 of cuqi/experimental/mcmc/_gibbs, the skip_len of the tune method is hardcoded to 1, meaning that the tuning of the scale parameter is always based on only the latest self._acc, i.e. either 0 or 1. This is not sensible for tuning. I suggest either using skip_len = max(int(0.1 * Nb), 1) which is the default in the warmup method in cuqi/experimental/mcmc/_sampler. Or letting it be user defined, again similar to the implementation in the warmup method in cuqi/experimental/mcmc/_sampler.

[siljachr]

The MH sampler did not append to self._acc, and therefore self._acc stayed at the initial value 1, which meant that the tune method increased the step length to the maximum (i.e. 1). I have pushed a small change that fixes this.

In line 220 of cuqi/experimental/mcmc/_gibbs, the skip_len of the tune method is hardcoded to 1, meaning that the tuning of the scale parameter is always based on only the latest self._acc, i.e. either 0 or 1. This is not sensible for tuning. I suggest either using skip_len = max(int(0.1 * Nb), 1) which is the default in the warmup method in cuqi/experimental/mcmc/_sampler. Or letting it be user defined, again similar to the implementation in the warmup method in cuqi/experimental/mcmc/_sampler.

I fixed an issue concerning how I first implemented appendence to self._acc. Now implemented in HybridGibbs instead of MH so it is also compatible with regular sampling (non-Gibbs), which already has appendence to self._acc implemented.

I have added the option of setting the tune_freq for HybridGibbs sampling, so it is no longer hard-coded. The implementation is equivalent to tune_freq in cuqi/experimental/mcmc/_sampler.

I have no further comments or concerns related to storing and using the acceptance rate in HybridGibbs :)

[amal-ghamdi]

Super!, many thanks @nabriis and @siljachr. Looks great.

I have a few comments. Feel free to address as you see fit.

[chaozg]

Thanks @nabriis and @siljachr for this nice PR. I just have a tiny reminder that the example in the docstring of HybridGibbs nees a bit update as it still follows the old way of sampling. I mean samples = sampler.sample(Ns=1000, Nb=200) here.

[chaozg]

LGTM. Regarding the issue of the example at the docstring of HybridGibbs, which is of course out the scope of this PR, I took the liberty of creating an issue to track it: #511

[amal-ghamdi]

Thank you @nabriis, I just added one comment regarding printing a warning for NUTS.

[amal-ghamdi]

LGTM!