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 2.7, 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 SMC 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 smcpy.examples.spring_mass.spring_mass_models import SpringMassModel
from smcpy.smc.smc_sampler import SMCSampler
# Load data
noise_stddev = 0.2
displacement_data = np.genfromtxt('noisy_data.txt')
# Initialize model
state0 = [0., 0.] #initial conditions
measure_t_grid = np.arange(0., 5., 0.2) #time
model = SpringMassModel(state0, measure_t_grid)
# Define prior distributions
param_priors = {'K': ['Uniform', 0.0, 10.0],
'g': ['Uniform', 0.0, 10.0]}
# SMC sampling
num_particles = 5000
num_time_steps = 20
num_mcmc_steps = 1
smc = SMCSampler(displacement_data, model, param_priors)
step_list = smc.sample(num_particles, num_time_steps, num_mcmc_steps, noise_stddev,
ess_threshold=num_particles*0.5)
if smc._rank == 0:
step_list[-1].plot_pairwise_weights(save=True)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 orange 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/).
The tests can be performed by running "py.test" from the tests/ directory to ensure a proper installation.
UQ Center of Excellence
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
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