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"""
Emcee and the Model Interface
=============================
"""
import corner
import matplotlib.pyplot as plt
import numpy as np
import lmfit
###############################################################################
# Set up a double-exponential function and create a Model
def double_exp(x, a1, t1, a2, t2):
return a1*np.exp(-x/t1) + a2*np.exp(-(x-0.1) / t2)
model = lmfit.Model(double_exp)
###############################################################################
# Generate some fake data from the model with added noise
truths = (3.0, 2.0, -5.0, 10.0)
x = np.linspace(1, 10, 250)
np.random.seed(0)
y = double_exp(x, *truths)+0.1*np.random.randn(x.size)
###############################################################################
# Create model parameters and give them initial values
p = model.make_params(a1=4, t1=3, a2=4, t2=3)
###############################################################################
# Fit the model using a traditional minimizer, and show the output:
result = model.fit(data=y, params=p, x=x, method='Nelder', nan_policy='omit')
lmfit.report_fit(result)
result.plot()
###############################################################################
# Calculate parameter covariance using emcee:
#
# - start the walkers out at the best-fit values
# - set is_weighted to False to estimate the noise weights
# - set some sensible priors on the uncertainty to keep the MCMC in check
#
emcee_kws = dict(steps=1000, burn=300, thin=20, is_weighted=False)
emcee_params = result.params.copy()
emcee_params.add('__lnsigma', value=np.log(0.1), min=np.log(0.001), max=np.log(2.0))
###############################################################################
# run the MCMC algorithm and show the results:
result_emcee = model.fit(data=y, x=x, params=emcee_params, method='emcee',
nan_policy='omit', fit_kws=emcee_kws)
lmfit.report_fit(result_emcee)
ax = plt.plot(x, model.eval(params=result.params, x=x), label='Nelder', zorder=100)
result_emcee.plot_fit(ax=ax, data_kws=dict(color='gray', markersize=2))
plt.show()
###############################################################################
# Plot the parameter covariances returned by emcee using corner
emcee_corner = corner.corner(result_emcee.flatchain, labels=result_emcee.var_names,
truths=list(result_emcee.params.valuesdict().values()))
###############################################################################
#
print("\nmedian of posterior probability distribution")
print('--------------------------------------------')
lmfit.report_fit(result_emcee.params)
# find the maximum likelihood solution
highest_prob = np.argmax(result_emcee.lnprob)
hp_loc = np.unravel_index(highest_prob, result_emcee.lnprob.shape)
mle_soln = result_emcee.chain[hp_loc]
print("\nMaximum likelihood Estimation")
print('-----------------------------')
for ix, param in enumerate(emcee_params):
print(param + ': ' + str(mle_soln[ix]))
quantiles = np.percentile(result_emcee.flatchain['t1'], [2.28, 15.9, 50, 84.2, 97.7])
print("\n\n1 sigma spread", 0.5 * (quantiles[3] - quantiles[1]))
print("2 sigma spread", 0.5 * (quantiles[4] - quantiles[0]))
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