# %%
# Seems that the linearity hypothesis is accurate.
# %%
# We complete this analysis using some usefull graphs :
# %%
fig = plt.figure(figsize=(12, 10))
for k, plot in enumerate([
"drawResidualsVsFitted", "drawScaleLocation", "drawQQplot",
"drawCookDistance", "drawResidualsVsLeverages", "drawCookVsLeverages"
]):
graph = getattr(analysis, plot)()
ax = fig.add_subplot(3, 2, k + 1)
v = View(graph, figure=fig, axes=[ax])
_ = v.getFigure().suptitle("Diagnostic graphs", fontsize=18)
# %%
# These graphics help asserting the linear model hypothesis. Indeed :
#
# - Quantile-to-quantile plot seems accurate
#
# - We notice heteroscedasticity within the noise
#
# - It seems that there is no outlier
# %%
# Finally we give the intervals for each estimated coefficient (95% confidence interval):
# %%
alpha = 0.95
title_2d = 'PDF of the Dirichlet dist. with theta = {}'
theta_1 = (2.0, 2.0, 2.0)
theta_2 = (0.5, 0.7, 0.9)
pdf_2d_1 = ot.Graph(title_2d.format(theta_1), 'x1', 'x2', True)
pdf_2d_2 = ot.Graph(title_2d.format(theta_2), 'x1', 'x2', True)
palette = ot.Drawable.BuildDefaultPalette(10)
list_theta = [(2, 2), (7, 5), (2, 6), (3, 4)]
for theta in list_theta:
distribution = ot.Dirichlet(theta)
pdf_curve = distribution.drawPDF()
cdf_curve = distribution.drawCDF()
pdf_graph.add(pdf_curve)
cdf_graph.add(cdf_curve)
pdf_graph.setColors([palette[i] for i in range(4)])
cdf_graph.setColors([palette[i] for i in range(4)])
pdf_graph.setLegends(['theta={}'.format(theta) for theta in list_theta])
cdf_graph.setLegends(['theta={}'.format(theta) for theta in list_theta])
distribution_2d_1 = ot.Dirichlet(theta_1)
distribution_2d_2 = ot.Dirichlet(theta_2)
pdf_2d_1.add(distribution_2d_1.drawPDF())
pdf_2d_2.add(distribution_2d_2.drawPDF())
grid.setGraph(0, 0, pdf_graph)
grid.setGraph(0, 1, cdf_graph)
grid.setGraph(1, 0, pdf_2d_1)
grid.setGraph(1, 1, pdf_2d_2)
grid.setTitle('Dirichlet (theta)')
grid.setLegendPosition('topright')
v = View(grid)
fig = v.getFigure()
fig.axes[1].legend(loc='best')