Details on EBS Code

Implementation

The Python example below samples a random variable from the uniform distribution U(0, 1).

The usage is simple:

• Import the class
• Initialise the EBS class
• Feed samples into EBS until the stopping condition is met
• Return the estimate

This version of EBS uses an absolute accuracy target, which is better suited than a relative accuracy target to random variables with an expectation value close to zero.

Unlike a sampling bound based on Hoeffding's inequality, EBS uses empirical information from the samples to provide tighter bounds in certain cases.

import numpy as np
from algorithms import EBS
a = 0
b = 1
delta = 0.1
epsilon = 0.01

ebs = EBS(epsilon=epsilon, delta=delta, range_of_rndvar=b - a)

while ebs.cond_check():
    ebs.add_sample(np.random.uniform(a, b))

print("Estimated mean:", ebs.get_estimate())
print("Number of samples taken:", round(ebs.get_num_samples()))
# Example output (values vary between runs):
# Estimated mean: 0.50
# Number of samples taken: 14978