Python module for uncertainty quantification using a parallel sequential Monte Carlo sampler.
To 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 calibration. SMC sampling can then be conducted with ease through instantiation of the SMCSampler class and a call to the sample() method. The output of this process is an approximation of the parameter posterior probability distribution conditional on the data provided.
The primary sampling algorithm implemented in this package is an MPI-enabled version of that presented in the following IEEE article by Nguyen et al.:
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
This software was funded by and developed under the High Performance Computing Incubator (HPCI) at NASA Langley Research Center.
import numpy as np
from scipy.stats import uniform
from spring_mass_model import SpringMassModel
from smcpy.utils.plotter import plot_pairwise
from smcpy import SMCSampler, VectorMCMC, VectorMCMCKernel
# Load data
std_dev = 0.5
displacement_data = np.genfromtxt('noisy_data.txt')
# Define prior distributions & MCMC kernel
priors = [uniform(0, 10), uniform(0, 10)]
vector_mcmc = VectorMCMC(model.evaluate, displacement_data, priors, std_dev)
mcmc_kernel = VectorMCMCKernel(vector_mcmc, param_order=('K', 'g'))
# SMC sampling
smc = SMCSampler(mcmc_kernel)
step_list, mll_list = smc.sample(num_particles=500,
num_mcmc_samples=5,
phi_sequence=np.linspace(0, 1, 20),
ess_threshold=0.8,
progress_bar=True)
# Display results
print(f'parameter means = {step_list[-1].compute_mean()}')
plot_pairwise(step_list[-1].params, step_list[-1].weights, save=True,
param_labels=['K', 'g'])The above code produces probabilistic estimates of K, the spring stiffness divided by mass, and g, the gravitational constant on an unknown planet. These estimates are in the form of weighted particles and can be visualized by plotting the pairwise weights as shown below. The mean of each parameter is marked by the dashed red line. The true values for this example were K = 1.67 and g = 4.62. More details can be found in the spring mass example (smcpy/examples/spring_mass/).
To run this model in parallel using MPI, the MCMC kernel just needs to be built with the ParallelMCMC class in place of VectorMCMC. More details can be found in the MPI example (smcpy/examples/mpi_example/).
The tests can be performed by running "pytest" from the tests/unit directory to ensure a proper installation.
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.
Contributors: Patrick Leser (patrick.e.leser@nasa.gov) and 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.
Disclaimers No Warranty: THE SUBJECT SOFTWARE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY OF ANY KIND, EITHER EXPRESSED, IMPLIED, OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, ANY WARRANTY THAT THE SUBJECT SOFTWARE WILL CONFORM TO SPECIFICATIONS, ANY IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, OR FREEDOM FROM INFRINGEMENT, ANY WARRANTY THAT THE SUBJECT SOFTWARE WILL BE ERROR FREE, OR ANY WARRANTY THAT DOCUMENTATION, IF PROVIDED, WILL CONFORM TO THE SUBJECT SOFTWARE. THIS AGREEMENT DOES NOT, IN ANY MANNER, CONSTITUTE AN ENDORSEMENT BY GOVERNMENT AGENCY OR ANY PRIOR RECIPIENT OF ANY RESULTS, RESULTING DESIGNS, HARDWARE, SOFTWARE PRODUCTS OR ANY OTHER APPLICATIONS RESULTING FROM USE OF THE SUBJECT SOFTWARE. FURTHER, GOVERNMENT AGENCY DISCLAIMS ALL WARRANTIES AND LIABILITIES REGARDING THIRD-PARTY SOFTWARE, IF PRESENT IN THE ORIGINAL SOFTWARE, AND DISTRIBUTES IT "AS IS."
Waiver and Indemnity: RECIPIENT AGREES TO WAIVE ANY AND ALL CLAIMS AGAINST THE UNITED STATES GOVERNMENT, ITS CONTRACTORS AND SUBCONTRACTORS, AS WELL AS ANY PRIOR RECIPIENT. IF RECIPIENT'S USE OF THE SUBJECT SOFTWARE RESULTS IN ANY LIABILITIES, DEMANDS, DAMAGES, EXPENSES OR LOSSES ARISING FROM SUCH USE, INCLUDING ANY DAMAGES FROM PRODUCTS BASED ON, OR RESULTING FROM, RECIPIENT'S USE OF THE SUBJECT SOFTWARE, RECIPIENT SHALL INDEMNIFY AND HOLD HARMLESS THE UNITED STATES GOVERNMENT, ITS CONTRACTORS AND SUBCONTRACTORS, AS WELL AS ANY PRIOR RECIPIENT, TO THE EXTENT PERMITTED BY LAW. RECIPIENT'S SOLE REMEDY FOR ANY SUCH MATTER SHALL BE THE IMMEDIATE, UNILATERAL TERMINATION OF THIS AGREEMENT.