SMC-NUTS

An SMC sampler with a No-U-Turn sampler proposal distribution

This is a codebase used to generate results when using the No-U-Turn Sampler (NUTS) as a proposal distribution for a sequential Monte Carlo (SMC) sampler. This algorithm has been designed to take a Stan model as input and use BridgeStan to evaluate the both evaluations of the log posterior and the associated gradient.

Installing SMC-NUTS

To install SMC-NUTS, follow these steps:

git clone https://github.com/UoL-SignalProcessingGroup/SMC-NUTS

cd SMC-NUTS

python3 -m pip install -e .

NOTE:

• The BridgeStan Pythonic interface to Stan must be installed in order to sample from Stan models (requirement > Python3.8).

pip install bridgestan

Using SMC-NUTS

An example is provided in the examples directory:

python run_experiments.py

This code will generate multiple results into the experiments/output/model_name for a model defined in stan_models. Results generated include: Mean estimates, variance estimates, effective sample size (ess), temperature (phi) schedule, and the acceptance probability.

Results can then be plotted by

python plot_experiments.py

Which will plot averaged results over all runs.

Defining an SMC sampler and its L-kernel strategy

An SMC sampler instance is created with the following call

SMC_NUTS= SMCSampler(
    K=K,
    N=N,
    target=target,
    forward_kernel=forward_kernel,
    sample_proposal=sample_proposal,
    tempering=tempering
    lkernel=forward_lkernel,
    verbose=VERBOSE,
    rng=rng,
)

Where K is the number of iterations the sampler is run over, N is the number of samples, target is a StanModel instance from Bridgestan, forward_kernel describes how samples are propagated inside the sampler, tempering describes the tempering strategy to be used, 'lkernel' tells the sampler what l-kernel to use and therefore which weight update needs to be implemented.

At present there are three strategies define the L-kernel in the SMC sampler

• An Asymptopic L-kernel which uses accept-reject
• An L-kernel parameterised by the Forwards proposal
• A Gaussian approximation to the Optimal-L-kernel

Please consult experiments/run_experiments.py to see examples of how this may be implemented in practice.

When using the asymptoptic L-kernel. The Stan model requires a temperature parameter (phi) in order to change the model with a tempered distribution. Consult examples to see instances of how this is done.

Future updates

• Adaptive learning of both the mass matrix and step-size utilised by the sampler.

Citation

We appreciate citations as they let us discover what people have been doing with the software.

To cite SMC-NUTS in publications use:

Devlin, L., Carter, M., Green, P.L., Maskell, S. (2023). SMC-NUTS (1.0.0). https://github.com//UoL-SignalProcessingGroup/SMC-NUTS

Or use the following BibTeX entry:

@misc{pysmc,
  title = {SMC-NUTS (1.0.0)},
  author = { Devlin, L., Carter, M., Green, P.L., Maskell, S.},
  year = {2023},
  month = September,
  howpublished = {GitHub},
  url = {https://github.com//UoL-SignalProcessingGroup/SMC-NUTS}
}