control_variates.ipynb

Kernel: Unknown Kernel

# Control variates demo
# https://en.wikipedia.org/wiki/Control_variates


import numpy as np

np.random.seed(0)

N = 1500
u = np.random.uniform(size=N)
f = 1 / (1 + u)
mu_naive = np.mean(f)
se_naive = np.sqrt(np.var(f) / N)
print("naive {:0.4f}, se {:0.4f}".format(mu_naive, se_naive))

# control variate version
c = 0.4773
g = 1 + u
baseline = 3.0 / 2
cv = f + c * (g - baseline)
mu_cv = np.mean(cv)
se_cv = np.sqrt(np.var(cv) / N)
print("cv {:0.4f}, se {:0.4f}".format(mu_cv, se_cv))