Bayes Decision Boundary

Figure 9.1

An illustration of a decision boundary between two Gaussian distributions.

Code output:

Python source code:

# Author: Jake VanderPlas
# License: BSD
#   The figure produced by this code is published in the textbook
#   "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)
#   For more information, see http://astroML.github.com
#   To report a bug or issue, use the following forum:
#    https://groups.google.com/forum/#!forum/astroml-general
import numpy as np
from matplotlib import pyplot as plt
from scipy.stats import norm

#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX.  This may
# result in an error if LaTeX is not installed on your system.  In that case,
# you can set usetex to False.
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)

#------------------------------------------------------------
# Compute the two PDFs
x = np.linspace(-3, 7, 1000)
pdf1 = norm(0, 1).pdf(x)
pdf2 = norm(3, 1.5).pdf(x)
x_bound = x[np.where(pdf1 < pdf2)][0]

#------------------------------------------------------------
# Plot the pdfs and decision boundary
fig = plt.figure(figsize=(5, 3.75))
ax = fig.add_subplot(111)
ax.plot(x, pdf1, '-k', lw=1)
ax.fill_between(x, pdf1, color='gray', alpha=0.5)

ax.plot(x, pdf2, '-k', lw=1)
ax.fill_between(x, pdf2, color='gray', alpha=0.5)

# plot decision boundary
ax.plot([x_bound, x_bound], [0, 0.5], '--k')

ax.text(x_bound + 0.2, 0.49, "decision boundary",
        ha='left', va='top', rotation=90)

ax.text(0, 0.2, '$g_1(x)$', ha='center', va='center')
        
ax.text(3, 0.1, '$g_2(x)$', ha='center', va='center')

ax.set_xlim(-2, 7)
ax.set_ylim(0, 0.5)

ax.set_xlabel('$x$')
ax.set_ylabel('$p(x)$')

plt.show()

[download source: fig_bayes_DB.py]