def animate(i, Z, max_lags):
line1.set_data(Z[:i, 0][::-1], range(len(Z[:i, 0])))
line2.set_data(range(len(Z[:i, 1])), Z[:i, 1][::-1])
line3.set_data(Z[:i, 0], Z[:i, 1])
line4.set_data(Z[:i, 0], Z[:i, 1])
line5.set_data([Z[i - 1, 0], Z[i - 1, 0]], [Z[i - 1, 1], s_width[1]])
line6.set_data([Z[i - 1, 0], i_width[1]], [Z[i - 1, 1], Z[i - 1, 1]])
# Calculate the ACF and plot on graph after some samples
if i >= samples * 0.10:
lags = np.arange(1, max_lags)
line7.set_data(lags, [autocorr(Z[:i, 0], l) for l in lags])
line8.set_data(lags, [autocorr(Z[:i, 1], l) for l in lags])
return lines
# ax.plot(posterior_small);
# _ = ax.set(xlabel='sample', ylabel='mu')
# plt.show()
# large width
posterior_large = sampler(data, samples=5000, mu_init=1., proposal_width=3.)
# fig, ax = plt.subplots()
# ax.plot(posterior_large); plt.xlabel('sample'); plt.ylabel('mu');
# _ = ax.set(xlabel='sample', ylabel='mu')
# plt.show()
from pymc3.stats import autocorr
lags = np.arange(1, 100)
fig, ax = plt.subplots()
ax.plot(lags, [autocorr(posterior_large, l) for l in lags], label='large step size')
ax.plot(lags, [autocorr(posterior_small, l) for l in lags], label='small step size')
ax.plot(lags, [autocorr(posterior, l) for l in lags], label='medium step size')
ax.legend(loc=0)
_ = ax.set(xlabel='lag', ylabel='autocorrelation', ylim=(-.1, 1))
import pymc3 as pm
with pm.Model():
mu = pm.Normal('mu', 0, 1)
sigma = 1.
returns = pm.Normal('returns', mu=mu, sd=sigma, observed=data)
step = pm.Metropolis()
trace = pm.sample(15000, step)
def autocorr(self, posterior_chain):
"""Produce autocorrelation plots"""
lags = np.arange(1, 250)
plt.plot(lags,
[autocorr(posterior_chain[self.burn_in:], l) for l in lags])
plt.show()
# plt.show()
# Plot too narow proposal width
posterior_small = sampler(data, samples=5000, mu_init=1., proposal_width=.01)
fig, ax = plt.subplots()
ax.plot(posterior_small)
_ = ax.set(xlabel='sample', ylabel='$T_{\mu}$')
# plt.show()
# Plot too wide proposal width proposal width
posterior_large = sampler(data, samples=5000, mu_init=1., proposal_width=3.)
fig, ax = plt.subplots()
ax.plot(posterior_large)
plt.xlabel('sample')
plt.ylabel('mu')
_ = ax.set(xlabel='sample', ylabel='$T_{\mu}$')
# plt.show()
from pymc3.stats import autocorr
lags = np.arange(1, 100)
fig, ax = plt.subplots()
ax.plot(lags, [autocorr(posterior_large, l) for l in lags],
label='Wide proposal width')
ax.plot(lags, [autocorr(posterior_small, l) for l in lags],
label='Narrow proposal width')
ax.plot(lags, [autocorr(posterior, l) for l in lags],
label='Medium proposal width')
ax.legend(loc=0)
_ = ax.set(xlabel='lag', ylabel='autocorrelation', ylim=(-.1, 1))
plt.show()