fit_vals = (M.b0.value, M.beta.value, M.A.value, M.omega.value)
return traces, fit_vals
traces, fit_vals = compute_MCMC_results()
labels = ['$b_0$', '$A$', r'$\omega$', r'$\beta$']
limits = [(9.5, 11.3), (3.6, 6.4), (0.065, 0.115), (0.00975, 0.01045)]
true = [b0_true, A_true, omega_true, beta_true]
#----------------------------------------------------------------------
# Find the Maximum a posteriori values
fig = plt.figure(figsize=(8, 8))
fig.subplots_adjust(bottom=0.1, top=0.95,
left=0.12, right=0.95,
hspace=0.05, wspace=0.05)
ax = plt.axes([0.5, 0.7, 0.45, 0.25])
t_fit = np.linspace(0, 100, 1001)
y_fit = chirp(t_fit, *fit_vals)
plt.scatter(t, y_obs, s=9, lw=0, c='k')
plt.plot(t_fit, y_fit, '-k')
plt.xlim(0, 100)
plt.xlabel('$t$')
plt.ylabel('$h_{obs}$')
# This function plots multiple panels with the traces
plot_mcmc(traces, labels=labels, limits=limits, true_values=true, fig=fig,
bins=30, colors='k', linewidths=2)
plt.show()
traces = [S.trace(s)[:] for s in ['T', 'A', 'omega', 'beta']]
return traces
traces = compute_MCMC()
labels = ['$T$', '$A$', r'$\omega$', r'$\beta$']
limits = [(29.75, 30.25), (0.75, 0.83), (0.085, 0.115), (0.0197, 0.0202)]
true = [T_true, A_true, omega_true, beta_true]
#------------------------------------------------------------
# Plot results
fig = plt.figure(figsize=(5, 5))
# This function plots multiple panels with the traces
axes_list = plot_mcmc(traces, labels=labels, limits=limits,
true_values=true, fig=fig,
bins=30, colors='k',
bounds=[0.14, 0.08, 0.95, 0.95])
for ax in axes_list:
for axis in [ax.xaxis, ax.yaxis]:
axis.set_major_locator(plt.MaxNLocator(5))
ax = fig.add_axes([0.52, 0.7, 0.43, 0.25])
ax.scatter(t, y_obs, s=9, lw=0, c='k')
ax.plot(t_fit, y_fit, '-k')
ax.set_xlim(0, 100)
ax.set_xlabel('$t$')
ax.set_ylabel(r'$h_{\rm obs}$')
plt.show()
#----------------------------------------------------------------------
# Find the Maximum a posteriori values
fig = plt.figure(figsize=(8, 8))
fig.subplots_adjust(bottom=0.1,
top=0.95,
left=0.12,
right=0.95,
hspace=0.05,
wspace=0.05)
ax = plt.axes([0.5, 0.7, 0.45, 0.25])
t_fit = np.linspace(0, 100, 1001)
y_fit = chirp(t_fit, *fit_vals)
plt.scatter(t, y_obs, s=9, lw=0, c='k')
plt.plot(t_fit, y_fit, '-k')
plt.xlim(0, 100)
plt.xlabel('$t$')
plt.ylabel('$h_{obs}$')
# This function plots multiple panels with the traces
plot_mcmc(traces,
labels=labels,
limits=limits,
true_values=true,
fig=fig,
bins=30,
colors='k',
linewidths=2)
plt.show()
traces = [S.trace(s)[:] for s in ['T', 'A', 'omega', 'beta']]
return traces
traces = compute_MCMC()
labels = ['$T$', '$A$', r'$\omega$', r'$\beta$']
limits = [(29.75, 30.25), (0.75, 0.83), (0.085, 0.115), (0.0197, 0.0202)]
true = [T_true, A_true, omega_true, beta_true]
#------------------------------------------------------------
# Plot results
fig = plt.figure(figsize=(8, 8))
# This function plots multiple panels with the traces
axes_list = plot_mcmc(traces, labels=labels, limits=limits,
true_values=true, fig=fig,
bins=30, colors='k', linewidths=2,
bounds=[0.14, 0.08, 0.95, 0.95])
for ax in axes_list:
for axis in [ax.xaxis, ax.yaxis]:
axis.set_major_locator(plt.MaxNLocator(5))
ax = fig.add_axes([0.5, 0.7, 0.45, 0.25])
ax.scatter(t, y_obs, s=9, lw=0, c='k')
ax.plot(t_fit, y_fit, '-k')
ax.set_xlim(0, 100)
ax.set_xlabel('$t$')
ax.set_ylabel('$h_{obs}$')
plt.show()
traces = compute_model()
labels = ['$r_0$', '$a$', r'$\phi$', r'$\omega$']
limits = [(6.5, 13.5), (0.55, 1.1), (-0.3, 1.7), (3.75, 4.25)]
true = [r0_true, a_true, phi_true, omega_true]
# ------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 5))
# This function plots multiple panels with the traces
plot_mcmc([traces[i]
for i in ['r0', 'a', 'phi']] + [np.exp(traces['log_omega'])],
labels=labels,
limits=limits,
true_values=true,
fig=fig,
bins=30,
colors='k')
# Plot the model of arrival times
ax = fig.add_axes([0.5, 0.75, 0.45, 0.2])
ax.fill_between(t,
0,
rate_func(t, r0_true, a_true, omega_true, phi_true),
facecolor='#DDDDDD',
edgecolor='black')
ax.xaxis.set_major_formatter(plt.NullFormatter())
ax.set_xlim(t[0], t[-1])
ax.set_ylim(0, 20)
ax.set_ylabel('$r(t)$')
traces, fit_vals = compute_MCMC_results()
labels = ['$b_0$', '$A$', r'$\omega$', r'$\beta$']
limits = [(9.5, 11.3), (3.6, 6.4), (0.065, 0.115), (0.00975, 0.01045)]
true = [b0_true, A_true, omega_true, beta_true]
#----------------------------------------------------------------------
# Find the Maximum a posteriori values
fig = plt.figure(figsize=(5, 5))
ax = plt.axes([0.5, 0.7, 0.45, 0.25])
t_fit = np.linspace(0, 100, 1001)
y_fit = chirp(t_fit, *fit_vals)
plt.scatter(t, y_obs, s=9, lw=0, c='k')
plt.plot(t_fit, y_fit, '-k')
plt.xlim(0, 100)
plt.xlabel('$t$')
plt.ylabel(r'$h_{\rm obs}$')
# This function plots multiple panels with the traces
plot_mcmc(traces,
labels=labels,
limits=limits,
true_values=true,
fig=fig,
bins=30,
bounds=[0.12, 0.08, 0.95, 0.91],
colors='k')
plt.show()
# ------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 5))
fig.subplots_adjust(bottom=0.1,
top=0.95,
left=0.1,
right=0.95,
hspace=0.05,
wspace=0.05)
# This function plots multiple panels with the traces
plot_mcmc([traces[i] for i in ['b0', 'A', 'T']] + [ssig(traces['log_ssig'])],
labels=labels,
limits=limits,
true_values=true,
fig=fig,
bins=30,
colors='k')
# plot the model fit
ax = fig.add_axes([0.5, 0.75, 0.45, 0.20])
t_fit = np.linspace(0, 100, 101)
y_fit = gauss(t_fit, **mean_vals)
ax.scatter(t, y_obs, s=9, lw=0, c='k')
ax.plot(t_fit, y_fit, '-k')
ax.plot(t, y_true, ls="--", c="r", lw=1)
ax.set_xlim(0, 100)
ax.set_xlabel('$time$')
ax.set_ylim(0, 25)
M = pymc.MAP(model)
M.fit()
fit_vals = (M.b0.value, M.beta.value, M.A.value, M.omega.value)
return traces, fit_vals
traces, fit_vals = compute_MCMC_results()
labels = ['$b_0$', '$A$', r'$\omega$', r'$\beta$']
limits = [(9.5, 11.3), (3.6, 6.4), (0.065, 0.115), (0.00975, 0.01045)]
true = [b0_true, A_true, omega_true, beta_true]
#----------------------------------------------------------------------
# Find the Maximum a posteriori values
fig = plt.figure(figsize=(5, 5))
ax = plt.axes([0.5, 0.7, 0.45, 0.25])
t_fit = np.linspace(0, 100, 1001)
y_fit = chirp(t_fit, *fit_vals)
plt.scatter(t, y_obs, s=9, lw=0, c='k')
plt.plot(t_fit, y_fit, '-k')
plt.xlim(0, 100)
plt.xlabel('$t$')
plt.ylabel(r'$h_{\rm obs}$')
# This function plots multiple panels with the traces
plot_mcmc(traces, labels=labels, limits=limits, true_values=true, fig=fig,
bins=30, bounds=[0.12, 0.08, 0.95, 0.91], colors='k')
plt.show()
traces = pm.sample(draws=5000, tune=2000, step=step)
labels = ['$T$', '$A$', r'$\omega$', r'$\beta$']
limits = [(29.75, 30.25), (0.75, 0.83), (0.085, 0.115), (0.0197, 0.0202)]
true = [T_true, A_true, omega_true, beta_true]
# ------------------------------------------------------------
# Plot results
fig = plt.figure(figsize=(5, 5))
# This function plots multiple panels with the traces
axes_list = plot_mcmc([traces[i] for i in ['T', 'A', 'omega', 'beta']],
labels=labels,
limits=limits,
true_values=true,
fig=fig,
bins=30,
colors='k',
bounds=[0.14, 0.08, 0.95, 0.95])
for ax in axes_list:
for axis in [ax.xaxis, ax.yaxis]:
axis.set_major_locator(plt.MaxNLocator(5))
ax = fig.add_axes([0.52, 0.7, 0.43, 0.25])
ax.scatter(t, y_obs, s=9, lw=0, c='k')
ax.plot(t_fit, y_fit, '-k')
ax.set_xlim(0, 100)
ax.set_xlabel('$t$')
ax.set_ylabel(r'$h_{\rm obs}$')
labels = ['$b_0$', '$A$', r'$\omega$', r'$\beta$']
limits = [(9.5, 11.3), (3.6, 6.4), (0.065, 0.115), (0.00975, 0.01045)]
true = [b0_true, A_true, omega_true, beta_true]
fig = plt.figure(figsize=(5, 5))
ax = plt.axes([0.5, 0.7, 0.45, 0.25])
t_fit = np.linspace(0, 100, 1001)
y_fit = chirp(t_fit, **mean_vals)
# ----------------------------------------------------------------------
# Plot multiple panels with the traces
plt.scatter(t, y_obs, s=9, lw=0, c='k')
plt.plot(t_fit, y_fit, '-k')
plt.xlim(0, 100)
plt.xlabel('$t$')
plt.ylabel(r'$h_{\rm obs}$')
plot_mcmc([traces[ii] for ii in ['b0', 'A']] +
[np.exp(traces['log_omega']),
np.exp(traces['log_beta'])],
labels=labels,
limits=limits,
true_values=true,
fig=fig,
bins=30,
bounds=[0.12, 0.08, 0.95, 0.91],
colors='k')
plt.show()
