def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Best-fit point
best_fit_x = stats.best_fit(self.chisq, self.xdata)
best_fit_y = stats.best_fit(self.chisq, self.ydata)
summary.append("Best-fit point (x,y): {}, {}".format(
best_fit_x, best_fit_y))
if opt.show_best_fit:
pm.plot_data(best_fit_x, best_fit_y, schemes.best_fit)
# Posterior mean
posterior_mean_x = stats.posterior_mean(self.posterior, self.xdata)
posterior_mean_y = stats.posterior_mean(self.posterior, self.ydata)
summary.append("Posterior mean (x,y): {}, {}".format(
posterior_mean_x, posterior_mean_y))
if opt.show_posterior_mean:
pm.plot_data(posterior_mean_x, posterior_mean_y,
schemes.posterior_mean)
pdf_data = two_dim.posterior_pdf(self.xdata,
self.ydata,
self.posterior,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
if opt.show_posterior_pdf:
pm.plot_image(pdf_data.pdf, opt.bin_limits, opt.plot_limits,
schemes.posterior)
levels = [
two_dim.critical_density(pdf_data.pdf, aa) for aa in opt.alpha
]
# Make sure pdf is correctly normalised.
pdf = pdf_data.pdf
pdf = pdf / pdf.sum()
if opt.show_credible_regions:
pm.plot_contour(pdf,
levels,
schemes.posterior,
bin_limits=opt.bin_limits)
# Add legend
pm.legend(opt.leg_title, opt.leg_position)
return self.plot_data(figure=fig, summary=summary)
def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Best-fit point
best_fit_x = stats.best_fit(self.chisq, self.xdata)
best_fit_y = stats.best_fit(self.chisq, self.ydata)
summary.append("Best-fit point (x,y): {}, {}".format(best_fit_x, best_fit_y))
if opt.show_best_fit:
pm.plot_data(best_fit_x, best_fit_y, schemes.best_fit)
# Posterior mean
posterior_mean_x = stats.posterior_mean(self.posterior, self.xdata)
posterior_mean_y = stats.posterior_mean(self.posterior, self.ydata)
summary.append("Posterior mean (x,y): {}, {}".format(posterior_mean_x, posterior_mean_y))
if opt.show_posterior_mean:
pm.plot_data(posterior_mean_x, posterior_mean_y, schemes.posterior_mean)
pdf_data = two_dim.posterior_pdf(
self.xdata,
self.ydata,
self.posterior,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
if opt.show_posterior_pdf:
pm.plot_image(
pdf_data.pdf,
opt.bin_limits,
opt.plot_limits,
schemes.posterior)
levels = [two_dim.critical_density(pdf_data.pdf, aa) for aa in opt.alpha]
# Make sure pdf is correctly normalised.
pdf = pdf_data.pdf
pdf = pdf / pdf.sum()
if opt.show_credible_regions:
pm.plot_contour(
pdf,
levels,
schemes.posterior,
bin_limits=opt.bin_limits)
# Add legend
pm.legend(opt.leg_title, opt.leg_position)
return self.plot_data(figure=fig, summary=summary)
def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Best-fit point
best_fit_x = stats.best_fit(self.chisq, self.xdata)
best_fit_y = stats.best_fit(self.chisq, self.ydata)
summary.append("Best-fit point (x,y): {}, {}".format(best_fit_x, best_fit_y))
if opt.show_best_fit:
pm.plot_data(best_fit_x, best_fit_y, schemes.best_fit)
# Posterior mean
posterior_mean_x = stats.posterior_mean(self.posterior, self.xdata)
posterior_mean_y = stats.posterior_mean(self.posterior, self.ydata)
summary.append("Posterior mean (x,y): {}, {}".format(posterior_mean_x, posterior_mean_y))
if opt.show_posterior_mean:
pm.plot_data(posterior_mean_x, posterior_mean_y, schemes.posterior_mean)
# Profile likelihood
prof_data = two_dim.profile_like(
self.xdata,
self.ydata,
self.chisq,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
if opt.show_prof_like:
pm.plot_image(
prof_data.prof_like,
opt.bin_limits,
opt.plot_limits,
schemes.prof_like)
levels = [two_dim.critical_prof_like(aa) for aa in opt.alpha]
if opt.show_conf_intervals:
pm.plot_contour(
prof_data.prof_like,
levels,
schemes.prof_like,
bin_limits=opt.bin_limits)
# Add legend
pm.legend(opt.leg_title, opt.leg_position)
return self.plot_data(figure=fig, summary=summary)
def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Best-fit point
best_fit_x = stats.best_fit(self.chisq, self.xdata)
best_fit_y = stats.best_fit(self.chisq, self.ydata)
summary.append("Best-fit point (x,y): {}, {}".format(
best_fit_x, best_fit_y))
if opt.show_best_fit:
pm.plot_data(best_fit_x, best_fit_y, schemes.best_fit)
# Posterior mean
posterior_mean_x = stats.posterior_mean(self.posterior, self.xdata)
posterior_mean_y = stats.posterior_mean(self.posterior, self.ydata)
summary.append("Posterior mean (x,y): {}, {}".format(
posterior_mean_x, posterior_mean_y))
if opt.show_posterior_mean:
pm.plot_data(posterior_mean_x, posterior_mean_y,
schemes.posterior_mean)
# Profile likelihood
prof_data = two_dim.profile_like(self.xdata,
self.ydata,
self.chisq,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
if opt.show_prof_like:
pm.plot_image(prof_data.prof_like, opt.bin_limits, opt.plot_limits,
schemes.prof_like)
levels = [two_dim.critical_prof_like(aa) for aa in opt.alpha]
if opt.show_conf_intervals:
pm.plot_contour(prof_data.prof_like,
levels,
schemes.prof_like,
bin_limits=opt.bin_limits)
# Add legend
pm.legend(opt.leg_title, opt.leg_position)
return self.plot_data(figure=fig, summary=summary)
def _summary(name, param, posterior, chi_sq):
"""
Find summary statistics for a single parameter.
:param name: Name of parameter
:type name: string
:param param: Data column of parameter
:type param:
:param posterior:
:type posterior:
:param chi_sq:
:type chi_sq:
:returns: List of summary statistics for a particular parameter
:rtype: list
"""
# Best-fit point
bestfit = stats.best_fit(chi_sq, param)
# Posterior mean
post_mean = stats.posterior_mean(posterior, param)
# Credible regions
pdf_data = one_dim.posterior_pdf(param,
posterior,
nbins=default("nbins"),
bin_limits=default("bin_limits")
)
lower_credible_region = one_dim.credible_region(pdf_data.pdf,
pdf_data.bin_centers,
alpha=default("alpha")[1],
region="lower")
upper_credible_region = one_dim.credible_region(pdf_data.pdf,
pdf_data.bin_centers,
alpha=default("alpha")[1],
region="upper")
summary = [name,
bestfit,
post_mean,
lower_credible_region,
upper_credible_region
]
return summary
def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Autoscale the y-axis.
ax.autoscale(axis='y')
# Posterior PDF. Norm by area if not showing profile likelihood,
# otherwise norm max value to one.
pdf_data = one_dim.posterior_pdf(
self.xdata,
self.posterior,
nbins=opt.nbins,
bin_limits=opt.bin_limits,
norm_area=False if opt.show_prof_like else True)
if opt.show_posterior_pdf:
pm.plot_data(pdf_data.bin_centers, pdf_data.pdf, schemes.posterior)
# Profile likelihood
prof_data = one_dim.prof_data(self.xdata,
self.chisq,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
if opt.show_prof_like:
pm.plot_data(prof_data.bin_centers, prof_data.prof_like,
schemes.prof_like)
# Height to plot the best-fit and posterior-mean points
point_height = 0.02 * pdf_data.pdf.max()
# Best-fit point
best_fit = stats.best_fit(self.chisq, self.xdata)
summary.append("Best-fit point: {}".format(best_fit))
if opt.show_best_fit:
pm.plot_data(best_fit, point_height, schemes.best_fit)
# Posterior mean
posterior_mean = stats.posterior_mean(self.posterior, self.xdata)
summary.append("Posterior mean: {}".format(posterior_mean))
if opt.show_posterior_mean:
pm.plot_data(posterior_mean, point_height, schemes.posterior_mean)
# Credible region
lower_credible_region = [
one_dim.credible_region(pdf_data.pdf,
pdf_data.bin_centers,
alpha=aa,
region="lower") for aa in opt.alpha
]
upper_credible_region = [
one_dim.credible_region(pdf_data.pdf,
pdf_data.bin_centers,
alpha=aa,
region="upper") for aa in opt.alpha
]
summary.append(
"Lower credible region: {}".format(lower_credible_region))
summary.append(
"Upper credible region: {}".format(upper_credible_region))
if opt.show_credible_regions:
# Plot the credible region line @ +10% of the max PDF value
cr_height = 1.1 * pdf_data.pdf.max()
for lower, upper, scheme in zip(lower_credible_region,
upper_credible_region,
schemes.credible_regions):
pm.plot_data([lower, upper], [cr_height, cr_height], scheme)
# Confidence interval
conf_intervals = [
one_dim.conf_interval(prof_data.prof_chi_sq,
prof_data.bin_centers,
alpha=aa) for aa in opt.alpha
]
for intervals, scheme in zip(conf_intervals, schemes.conf_intervals):
if opt.show_conf_intervals:
# Plot the CI line @ the max PDF value
pm.plot_data(intervals, [pdf_data.pdf.max()] * int(opt.nbins),
scheme)
summary.append("{}:".format(scheme.label))
for interval in intervals:
summary.append(str(interval))
# Add plot legend
pm.legend(opt.leg_title, opt.leg_position)
# Override y-axis label. This prevents the y axis from taking its
# label from the 'y-axis variable' selction in the GUI.
if opt.show_posterior_pdf and not opt.show_prof_like:
plt.ylabel(schemes.posterior.label)
elif opt.show_prof_like and not opt.show_posterior_pdf:
plt.ylabel(schemes.prof_like.label)
else:
plt.ylabel("")
return self.plot_data(figure=fig, summary=summary)
def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Best-fit point
best_fit_x = stats.best_fit(self.chisq, self.xdata)
best_fit_y = stats.best_fit(self.chisq, self.ydata)
summary.append("Best-fit point (x,y): {}, {}".format(
best_fit_x, best_fit_y))
if opt.show_best_fit:
pm.plot_data(best_fit_x, best_fit_y, schemes.best_fit)
# Posterior mean
posterior_mean_x = stats.posterior_mean(self.posterior, self.xdata)
posterior_mean_y = stats.posterior_mean(self.posterior, self.ydata)
summary.append("Posterior mean (x,y): {}, {}".format(
posterior_mean_x, posterior_mean_y))
if opt.show_posterior_mean:
pm.plot_data(posterior_mean_x, posterior_mean_y,
schemes.posterior_mean)
# Plot scatter of points.
sc = plt.scatter(self.xdata,
self.ydata,
s=schemes.scatter.size,
c=self.zdata,
marker=schemes.scatter.symbol,
cmap=schemes.scatter.colour_map,
norm=None,
vmin=None,
vmax=None,
alpha=0.5,
linewidths=None,
verts=None)
# Plot a colour bar
cb = plt.colorbar(sc, orientation='horizontal', shrink=0.5)
# Colour bar label
cb.ax.set_xlabel(opt.zlabel)
# Set reasonable number of ticks
cb.locator = MaxNLocator(4)
cb.update_ticks()
# Credible regions
pdf_data = two_dim.posterior_pdf(self.xdata,
self.ydata,
self.posterior,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
levels = [
two_dim.critical_density(pdf_data.pdf, aa) for aa in opt.alpha
]
# Make sure pdf is correctly normalised
pdf = pdf_data.pdf
pdf = pdf / pdf.sum()
if opt.show_credible_regions:
pm.plot_contour(pdf,
levels,
schemes.posterior,
bin_limits=opt.bin_limits)
# Confidence interval
prof_data = two_dim.profile_like(self.xdata,
self.ydata,
self.chisq,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
levels = [two_dim.critical_prof_like(aa) for aa in opt.alpha]
if opt.show_conf_intervals:
pm.plot_contour(prof_data.prof_like,
levels,
schemes.prof_like,
bin_limits=opt.bin_limits)
# Add legend
pm.legend(opt.leg_title, opt.leg_position)
return self.plot_data(figure=fig, summary=summary)
def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Data itself.
prof_data = one_dim.prof_data(self.xdata,
self.chisq,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
# Plot the delta chi-squared
pm.plot_data(prof_data.bin_centers, prof_data.prof_chi_sq,
schemes.prof_chi_sq)
# Alter the y-axis limit so that it extends to 10.
opt.plot_limits[3] = 10.
pm.plot_limits(ax, opt.plot_limits)
# Best-fit point
best_fit = stats.best_fit(self.chisq, self.xdata)
summary.append("Best-fit point: {}".format(best_fit))
if opt.show_best_fit:
pm.plot_data(best_fit, 0.08, schemes.best_fit)
# Confidence intervals as filled regions
critical_chi_sq = [chi2.ppf(1. - aa, 1) for aa in opt.alpha]
for chi_sq, facecolor, name in zip(critical_chi_sq,
schemes.prof_chi_sq.colours,
schemes.prof_chi_sq.level_names):
# Create a list where element i is True if bin i should be filled.
fill_where = prof_data.prof_chi_sq >= chi_sq
# Fill in areas on the chart above the threshold
if opt.show_conf_intervals:
ax.fill_between(prof_data.bin_centers,
0,
10,
where=fill_where,
facecolor=facecolor,
interpolate=False,
alpha=0.7)
# List the boundaries of the regions that were filled in the summary file
# as comma separated pairs. itertools.groupby splits the list into
# contiguous regions according to the key function - we take the first
# and last elements of the "True" regions.
summary.append(name + ":")
for filled, group in groupby(zip(prof_data.bin_centers,
fill_where),
key=lambda x: x[1]):
if filled:
bins = [g[0] for g in group]
summary.append("{},{}".format(min(bins), max(bins)))
# Plot a proxy for the legend - plot spurious data outside plot limits,
# with legend entry matching colours of filled regions.
if opt.show_conf_intervals:
plt.plot(-1,
-1,
's',
color=facecolor,
label=name,
alpha=0.7,
ms=15)
if opt.tau is not None:
# Plot the theory error as a band around the usual line
pm.plot_band(prof_data.bin_centers, prof_data.prof_chi_sq, opt.tau,
ax, schemes.tau_band)
# Add plot legend
pm.legend(opt.leg_title, opt.leg_position)
# Override y-axis label. This prevents the y axis from taking its
# label from the 'y-axis variable' selction in the GUI (as
# in this plot it should always be chi-squared).
plt.ylabel(schemes.prof_chi_sq.label)
return self.plot_data(figure=fig, summary=summary)
def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Autoscale the y-axis.
ax.autoscale(axis='y')
# Posterior PDF. Norm by area if not showing profile likelihood,
# otherwise norm max value to one.
pdf_data = one_dim.posterior_pdf(self.xdata,
self.posterior,
nbins=opt.nbins,
bin_limits=opt.bin_limits,
norm_area=
False if opt.show_prof_like
else True)
if opt.show_posterior_pdf:
pm.plot_data(pdf_data.bin_centers, pdf_data.pdf, schemes.posterior)
# Profile likelihood
prof_data = one_dim.prof_data(self.xdata,
self.chisq,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
if opt.show_prof_like:
pm.plot_data(prof_data.bin_centers, prof_data.prof_like, schemes.prof_like)
# Height to plot the best-fit and posterior-mean points
point_height = 0.02 * pdf_data.pdf.max()
# Best-fit point
best_fit = stats.best_fit(self.chisq, self.xdata)
summary.append("Best-fit point: {}".format(best_fit))
if opt.show_best_fit:
pm.plot_data(best_fit, point_height, schemes.best_fit)
# Posterior mean
posterior_mean = stats.posterior_mean(self.posterior, self.xdata)
summary.append("Posterior mean: {}".format(posterior_mean))
if opt.show_posterior_mean:
pm.plot_data(posterior_mean, point_height, schemes.posterior_mean)
# Credible region
lower_credible_region = [one_dim.credible_region(pdf_data.pdf, pdf_data.bin_centers, alpha=aa, region="lower")
for aa in opt.alpha]
upper_credible_region = [one_dim.credible_region(pdf_data.pdf, pdf_data.bin_centers, alpha=aa, region="upper")
for aa in opt.alpha]
summary.append("Lower credible region: {}".format(lower_credible_region))
summary.append("Upper credible region: {}".format(upper_credible_region))
if opt.show_credible_regions:
# Plot the credible region line @ +10% of the max PDF value
cr_height = 1.1 * pdf_data.pdf.max()
for lower, upper, scheme in zip(lower_credible_region, upper_credible_region, schemes.credible_regions):
pm.plot_data([lower, upper], [cr_height, cr_height], scheme)
# Confidence interval
conf_intervals = [one_dim.conf_interval(prof_data.prof_chi_sq, prof_data.bin_centers, alpha=aa) for aa in
opt.alpha]
for intervals, scheme in zip(conf_intervals, schemes.conf_intervals):
if opt.show_conf_intervals:
# Plot the CI line @ the max PDF value
pm.plot_data(intervals, [pdf_data.pdf.max()] * int(opt.nbins), scheme)
summary.append("{}:".format(scheme.label))
for interval in intervals:
summary.append(str(interval))
# Add plot legend
pm.legend(opt.leg_title, opt.leg_position)
# Override y-axis label. This prevents the y axis from taking its
# label from the 'y-axis variable' selction in the GUI.
if opt.show_posterior_pdf and not opt.show_prof_like:
plt.ylabel(schemes.posterior.label)
elif opt.show_prof_like and not opt.show_posterior_pdf:
plt.ylabel(schemes.prof_like.label)
else:
plt.ylabel("")
return self.plot_data(figure=fig, summary=summary)
def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Best-fit point
best_fit_x = stats.best_fit(self.chisq, self.xdata)
best_fit_y = stats.best_fit(self.chisq, self.ydata)
summary.append("Best-fit point (x,y): {}, {}".format(best_fit_x, best_fit_y))
if opt.show_best_fit:
pm.plot_data(best_fit_x, best_fit_y, schemes.best_fit)
# Posterior mean
posterior_mean_x = stats.posterior_mean(self.posterior, self.xdata)
posterior_mean_y = stats.posterior_mean(self.posterior, self.ydata)
summary.append("Posterior mean (x,y): {}, {}".format(posterior_mean_x, posterior_mean_y))
if opt.show_posterior_mean:
pm.plot_data(posterior_mean_x, posterior_mean_y, schemes.posterior_mean)
# Plot scatter of points.
sc = plt.scatter(
self.xdata,
self.ydata,
s=schemes.scatter.size,
c=self.zdata,
marker=schemes.scatter.symbol,
cmap=schemes.scatter.colour_map,
norm=None,
vmin=None,
vmax=None,
alpha=0.5,
linewidths=None,
verts=None)
# Plot a colour bar
cb = plt.colorbar(sc, orientation='horizontal', shrink=0.5)
# Colour bar label
cb.ax.set_xlabel(opt.zlabel)
# Set reasonable number of ticks
cb.locator = MaxNLocator(4)
cb.update_ticks()
# Credible regions
pdf_data = two_dim.posterior_pdf(
self.xdata,
self.ydata,
self.posterior,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
levels = [two_dim.critical_density(pdf_data.pdf, aa) for aa in opt.alpha]
# Make sure pdf is correctly normalised
pdf = pdf_data.pdf
pdf = pdf / pdf.sum()
if opt.show_credible_regions:
pm.plot_contour(
pdf,
levels,
schemes.posterior,
bin_limits=opt.bin_limits)
# Confidence interval
prof_data = two_dim.profile_like(
self.xdata,
self.ydata,
self.chisq,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
levels = [two_dim.critical_prof_like(aa) for aa in opt.alpha]
if opt.show_conf_intervals:
pm.plot_contour(
prof_data.prof_like,
levels,
schemes.prof_like,
bin_limits=opt.bin_limits)
# Add legend
pm.legend(opt.leg_title, opt.leg_position)
return self.plot_data(figure=fig, summary=summary)
def figure(self):
fig, ax = self._new_plot()
opt = self.plot_options
summary = []
# Data itself.
prof_data = one_dim.prof_data(self.xdata,
self.chisq,
nbins=opt.nbins,
bin_limits=opt.bin_limits)
# Plot the delta chi-squared
pm.plot_data(prof_data.bin_centers, prof_data.prof_chi_sq, schemes.prof_chi_sq)
# Alter the y-axis limit so that it extends to 10.
opt.plot_limits[3] = 10.
pm.plot_limits(ax, opt.plot_limits)
# Best-fit point
best_fit = stats.best_fit(self.chisq, self.xdata)
summary.append("Best-fit point: {}".format(best_fit))
if opt.show_best_fit:
pm.plot_data(best_fit, 0.08, schemes.best_fit)
# Confidence intervals as filled regions
critical_chi_sq = [chi2.ppf(1. - aa, 1) for aa in opt.alpha]
for chi_sq, facecolor, name in zip(critical_chi_sq, schemes.prof_chi_sq.colours,
schemes.prof_chi_sq.level_names):
# Create a list where element i is True if bin i should be filled.
fill_where = prof_data.prof_chi_sq >= chi_sq
# Fill in areas on the chart above the threshold
if opt.show_conf_intervals:
ax.fill_between(prof_data.bin_centers,
0,
10,
where=fill_where,
facecolor=facecolor,
interpolate=False,
alpha=0.7
)
# List the boundaries of the regions that were filled in the summary file
# as comma separated pairs. itertools.groupby splits the list into
# contiguous regions according to the key function - we take the first
# and last elements of the "True" regions.
summary.append(name + ":")
for filled, group in groupby(zip(prof_data.bin_centers, fill_where), key=lambda x: x[1]):
if filled:
bins = [g[0] for g in group]
summary.append("{},{}".format(min(bins), max(bins)))
# Plot a proxy for the legend - plot spurious data outside plot limits,
# with legend entry matching colours of filled regions.
if opt.show_conf_intervals:
plt.plot(-1, -1, 's', color=facecolor, label=name, alpha=0.7, ms=15)
if opt.tau is not None:
# Plot the theory error as a band around the usual line
pm.plot_band(prof_data.bin_centers, prof_data.prof_chi_sq, opt.tau, ax, schemes.tau_band)
# Add plot legend
pm.legend(opt.leg_title, opt.leg_position)
# Override y-axis label. This prevents the y axis from taking its
# label from the 'y-axis variable' selction in the GUI (as
# in this plot it should always be chi-squared).
plt.ylabel(schemes.prof_chi_sq.label)
return self.plot_data(figure=fig, summary=summary)