neymanPearson2.ipynb

Kernel: Unknown Kernel

# Convert Neyman-Pearson testing paradigm(Fig 5.15 (a)) to python/JAX
# Author: Garvit9000c


from scipy.stats import multivariate_normal as gaussprob
import numpy as np
import matplotlib.pyplot as plt

try:
    import probml_utils as pml
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    import probml_utils as pml

# constants
pi = np.pi
sigma = 1.5
xmin = -4
xmax = 8
ymin = 0
ymax = 0.3
res = 0.01

# Domain
x = np.arange(xmin, xmax, res)

# functions
y1 = gaussprob.pdf(x, 0, sigma**2)
y2 = gaussprob.pdf(x, 4, sigma**2)

# Axes Limits
plt.ylim(ymin, ymax)
plt.xlim(xmin, xmax)

# Ploting Curve
plt.plot(x, y1, "b")  # Curve_B
plt.plot(x, y2, "r")  # Curve_A


plt.vlines(x=2.3, ymin=0, ymax=0.5, linewidth=1.5, color="k")
plt.xticks([2.3], ["$X^*$"], size=18)
plt.yticks([])

# Shading α Region
x1 = np.arange(2.3, xmax, res)
y_1 = gaussprob.pdf(x1, 0, sigma**2)
plt.fill_between(x1, y_1, 0, alpha=0.50)

# Shading β Region
x2 = np.arange(xmin, 2.3, res)
y_2 = gaussprob.pdf(x2, 4, sigma**2)
plt.fill_between(x2, y_2, 0, alpha=0.50)

# Axis Arrows
plt.arrow(0, 0.07, 1.2, -0.05, color="black", head_width=0.02, head_length=0.2)  # β
plt.arrow(4, 0.07, -1.2, -0.05, color="black", head_width=0.02, head_length=0.2)  # α

# label
plt.text(-0.4, 0.07, r"$\beta$", fontsize=15)  # β
plt.text(4, 0.07, r"$\alpha$", fontsize=15)  # α
plt.text(-0.2, 0.28, "$H_0$", fontsize=15)  # H0
plt.text(3.8, 0.28, "$H_1$", fontsize=15)  # H1

pml.savefig("neymanPearson2.pdf")
plt.show()