antithetic_sampling.ipynb

Kernel: Unknown Kernel

# demo of antithetic sampling
# https://en.wikipedia.org/wiki/Antithetic_variates


import numpy as np

np.random.seed(0)

N = 750  # 1500
u1 = np.random.uniform(size=N)
u2 = np.random.uniform(size=N)
u = np.concatenate((u1, u2))
f = 1 / (1 + u)
mu_naive = np.mean(f)
se_naive = np.sqrt(np.var(f) / (2 * N))
print("naive {:0.4f}, se {:0.4f}".format(mu_naive, se_naive))

# antithetic version
uprime = 1 - u1
f1 = 1 / (1 + u1)
fprime = 1 / (1 + uprime)
f = (f1 + fprime) / 2.0  # paired samples!
mu_anti = np.mean(f)
se_anti = np.sqrt(np.var(f) / (2 * N))
print("anti {:0.4f}, se {:0.4f}".format(mu_anti, se_anti))