This example shows you how to perform Bayesian inference on a time series, using DREAM MCMC.
It follows on from the first sampling example.
In [2]:
from __future__ import print_function
import pints
import pints.toy as toy
import pints.plot
import numpy as np
import matplotlib.pyplot as plt
# Load a forward model
model = toy.LogisticModel()
# Create some toy data
real_parameters = [0.015, 500]
times = np.linspace(0, 1000, 1000)
org_values = model.simulate(real_parameters, times)
# Add noise
noise = 10
values = org_values + np.random.normal(0, noise, org_values.shape)
real_parameters = np.array(real_parameters + [noise])
# Get properties of the noise sample
noise_sample_mean = np.mean(values - org_values)
noise_sample_std = np.std(values - org_values)
# Create an object with links to the model and time series
problem = pints.SingleOutputProblem(model, times, values)
# Show the noisy data
plt.figure()
plt.plot(times, values)
plt.show()
In [3]:
# Create a log-likelihood function (adds an extra parameter!)
log_likelihood = pints.GaussianLogLikelihood(problem)
# Create a uniform prior over both the parameters and the new noise variable
log_prior = pints.UniformLogPrior(
[0.01, 400, noise * 0.1],
[0.02, 600, noise * 100]
)
# Create a posterior log-likelihood
log_posterior = pints.LogPosterior(log_likelihood, log_prior)
# Create a differential evolution MCMC routine
x0 = [
real_parameters * 0.8,
real_parameters * 0.9,
real_parameters * 1.1,
]
mcmc = pints.MCMCController(log_posterior, 3, x0, method=pints.DreamMCMC)
mcmc.set_initial_phase_iterations(500)
mcmc.set_max_iterations(1000)
mcmc.set_log_to_screen(False)
Run!
In [4]:
# Run!
print('Running...')
chains = mcmc.run()
print('Done!')
In [5]:
pints.plot.trace(chains)
plt.show()
In [9]:
# Plot output
stacked = np.vstack(chains[:, 200::5])
pints.plot.pairwise(stacked, kde=True)
plt.show()
In [8]:
print(pints.rhat_all_params(chains[:, 200:]))