SMCPy is an open-source package for performing uncertainty quantification using a parallelized sequential Monte Carlo sampler.
- Alternative to Markov chain Monte Carlo for Bayesian inference problems
- Unbiased estimation of marginal likelihood for Bayesian model selection
- Parallelization through either numpy vectorization or mpi4py
To install SMCPy, use pip.
pip install smcpyTo operate the code, the user supplies a computational model built in Python 3.6+, defines prior distributions for each of the model parameters to be estimated, and provides data to be used for probabilistic model calibration. SMC sampling of the parameter posterior distribution can then be conducted with ease through instantiation of a sampler class and a call to the sample() method.
The two primary sampling algorithms implemented in this package are MPI-enabled versions of those presented in the following articles, respectively:
Nguyen, Thi Le Thu, et al. "Efficient sequential Monte-Carlo samplers for Bayesian inference." IEEE Transactions on Signal Processing 64.5 (2015): 1305-1319. Link to Article | BibTeX Reference
Buchholz, Alexander, Nicolas Chopin, and Pierre E. Jacob. "Adaptive tuning of hamiltonian monte carlo within sequential monte carlo." Bayesian Analysis 1.1 (2021): 1-27. Link to Article | BibTeX Reference
The first is a simple likelihood tempering approach in which the tempering sequence is fixed and user-specified (FixedPhiSampler). The second is an adaptive approach that chooses the tempering steps based on a target effective sample size (AdaptiveSampler).
This software was funded by and developed under the High Performance Computing Incubator (HPCI) at NASA Langley Research Center.
We'll set up a toy example: estimating the slope and intercept of a line given only noisy observations of points along that line.
import numpy as np
import seaborn as sns
import pandas as pd
from scipy.stats import uniform
from smcpy import AdaptiveSampler, VectorMCMC, VectorMCMCKernel
from smcpy.utils.noise_generator import generate_noisy_data
def model(params):
return params[:, [0]] * np.linspace(0.5, 2.5, 100) + params[:, [1]]
if __name__ == "__main__":
std_dev = 0.5
true_params = np.array([[2, 3.5]]) # true but unknown (to be estimated)
noisy_data = generate_noisy_data(model(true_params), std_dev)
priors = [uniform(-6, 12.0), uniform(-6, 12.0)]
vector_mcmc = VectorMCMC(model, noisy_data, priors, std_dev)
mcmc_kernel = VectorMCMCKernel(vector_mcmc, ("slope", "intercept"))
smc = AdaptiveSampler(mcmc_kernel)
step_list, mll_list = smc.sample(num_particles=500, num_mcmc_samples=10)
print(f"marginal log likelihood = {mll_list[-1]}")
print(f"parameter means = {step_list[-1].compute_mean()}")
sns.pairplot(pd.DataFrame(step_list[-1].param_dict))
sns.mpl.pyplot.savefig("pairwise.png")[ mutation ratio: 1.0: : 100.00%|███████████████████████████████████████| phi: 1.00000/1.0 [00:00<00:00
marginal log likelihood = -76.27987428009173
parameter means = {'slope': np.float64(2.0148875448007013), 'intercept': np.float64(3.523915137965013)}Plotting is easy with seaborn:
To run this example in parallel using MPI, the MCMC kernel just needs to be built with the
ParallelVectorMCMC class in place of VectorMCMC. More details can be found in the
MPI example.
Clone the repo and move into the package directory:
git clone https://github.com/nasa/SMCPy.git
cd SMCPyInstall requirements necessary to use SMCPy:
pip install -r requirements.txtOptionally, if you'd like to use the MPI-enabled parallel sampler, install the associated requirements:
pip install -r requirements_optional.txtAdd SMCPy to your Python path. For example:
export PYTHONPATH="$PYTHONPATH:/path/to/smcpy"Run the tests to ensure proper installation:
pytest tests- Fork (https://github.com/nasa/SMCPy/fork)
- Create your feature branch (
git checkout -b feature/fooBar) - Commit your changes (
git commit -am 'Add some fooBar') - Push to the branch (
git push origin feature/fooBar) - Create a Pull Request
NASA Langley Research Center
Hampton, Virginia
This software was funded by and developed under the High Performance Computing Incubator (HPCI) at NASA Langley Research Center.
- Patrick Leser
- Julia Truong
- Michael Wang
Notices: Copyright 2018 United States Government as represented by the Administrator of the National Aeronautics and Space Administration. No copyright is claimed in the United States under Title 17, U.S. Code. All Other Rights Reserved.
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