shawlu95

import numpy as np
engagement = np.loadtxt('data/engagement.csv')

mean = np.mean(engagement)
std = np.std(engagement)

print("""
Population mean: %.5f
Population std: %.5f
Population size: %i

shawlu95

sample_size = 300
n_trials = 1000000

# draw one million samples, each of size 300
samples = np.array([np.random.choice(engagement, sample_size) 
                    for _ in range(n_trials)])
                    
# calculate sample mean for each sample
means = samples.mean(axis=1)

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# make 95% confidence interval
z = 1.96

se = samples.std(axis=1) / np.sqrt(sample_size)
ups = means + z * se
los = means - z * se

success = np.mean((mean >= los) & (mean <= ups))
fpr = np.mean((mean < los) | (mean > ups))

shawlu95

import numpy as np
from scipy.stats import beta

a1, b1 = 10, 10
rv1 = beta(a1, b1)

a2, b2 = 3, 3
rv2 = beta(a2, b2)

x = np.linspace(0, 1, 100)

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class Arm(object):
    """
    Each arm's true click through rate is 
    modeled by a beta distribution.
    """
    def __init__(self, idx, a=1, b=1):
        """
        Init with uniform prior.
        """
        self.idx = idx

shawlu95

def monte_carlo_simulation(arms, draw=100):
    """
    Monte Carlo simulation of thetas. Each arm's click through
    rate follows a beta distribution.
    
    Parameters
    ----------
    arms list[Arm]: list of Arm objects.
    draw int: number of draws in Monte Carlo simulation.
    

shawlu95

def thompson_sampling(arms):
    """
    Stochastic sampling: take one draw for each arm
    divert traffic to best draw.
    
    @param arms list[Arm]: list of Arm objects
    @return idx int: index of winning arm from sample
    """
    sample_p = [arm.draw_ctr() for arm in arms]
    idx = np.argmax(sample_p)

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def should_terminate(p_winner, est_ctrs, mc, alpha=0.05):
    """
    Decide whether experiument should terminate. When value remaining in
    experiment is less than 1% of the winning arm's click through rate.
    
    Parameters
    ----------
    p_winner list[float]: probability of each arm being the winner.
    est_ctrs list[float]: estimated click through rates.
    mc np.matrix: Monte Carlo matrix of dimension (draw, n_arms).

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def k_arm_bandit(ctrs, alpha=0.05, burn_in=1000, max_iter=100000, draw=100, silent=False):
    """
    Perform stochastic k-arm bandit test. Experiment is terminated when
    value remained in experiment drops below certain threshold.
    
    Parameters
    ----------
    ctrs list[float]: true click through rates for each arms.
    alpha float: terminate experiment when the (1 - alpha)th percentile
        of the remaining value is less than 1% of the winner's click through rate.

shawlu95

def critical_z(alpha=0.05, tail="two"):
    """
    Given significance level, compute critical value.
    """
    if tail == "two":
        p = 1 - alpha / 2
    else:
        p = 1 - alpha
        
    return norm.ppf(p)