def bayesian_log_normal_with_0_test (A_data, B_data, m0, k0,s_sq0, v0, mean_lift = 0):
# modeling zero vs. non-zero
non_zeros_A = sum(A_data > 0)
total_A = len(A_data)
non_zeros_B = sum(B_data > 0)
total_B = len(B_data)
alpha = 1 # uniform prior
beta = 1
n_samples = 10000 # number of samples to draw
A_conv_samps = beta_dist(non_zeros_A+alpha, total_A-non_zeros_A+beta, n_samples)
B_conv_samps = beta_dist(non_zeros_B+alpha, total_B-non_zeros_B+beta, n_samples)
# modeling the non-zeros with a log-normal
A_non_zero_data = A_data[A_data > 0]
B_non_zero_data = B_data[B_data > 0]
A_order_samps = draw_log_normal_means(A_non_zero_data,m0,k0,s_sq0,v0)
B_order_samps = draw_log_normal_means(B_non_zero_data,m0,k0,s_sq0,v0)
# combining the two
A_rps_samps = A_conv_samps*A_order_samps
B_rps_samps = B_conv_samps*B_order_samps
# the result
print mean(A_rps_samps > B_rps_samps)
def bayesian_log_normal_with_0_test(A_data,
B_data,
m0,
k0,
s_sq0,
v0,
mean_lift=0):
# modeling zero vs. non-zero
non_zeros_A = sum(A_data > 0)
total_A = len(A_data)
non_zeros_B = sum(B_data > 0)
total_B = len(B_data)
alpha = 1 # uniform prior
beta = 1
n_samples = 10000 # number of samples to draw
A_conv_samps = beta_dist(non_zeros_A + alpha, total_A - non_zeros_A + beta,
n_samples)
B_conv_samps = beta_dist(non_zeros_B + alpha, total_B - non_zeros_B + beta,
n_samples)
# modeling the non-zeros with a log-normal
A_non_zero_data = A_data[A_data > 0]
B_non_zero_data = B_data[B_data > 0]
A_order_samps = draw_log_normal_means(A_non_zero_data, m0, k0, s_sq0, v0)
B_order_samps = draw_log_normal_means(B_non_zero_data, m0, k0, s_sq0, v0)
# combining the two
A_rps_samps = A_conv_samps * A_order_samps
B_rps_samps = B_conv_samps * B_order_samps
# the result
print mean(A_rps_samps > B_rps_samps)
def calc_beta_prob(df_grouped, num_samples=100000):
#perform bayesian test to simulate future data distributions
clicks_new = df_grouped[df_grouped['optimum'] == 1]['clicked']
view_new = df_grouped[df_grouped['optimum'] == 1]['counter']
clicks_old = df_grouped[df_grouped['optimum'] == 0]['clicked']
view_old = df_grouped[df_grouped['optimum'] == 0]['counter']
new_samples = beta_dist(1 + clicks_new, 1 + view_new - clicks_new,
num_samples)
old_samples = beta_dist(1 + clicks_old, 1 + view_old - clicks_old,
num_samples)
return np.mean(new_samples - old_samples > .015)
def calculate_statistics(pool, events, samples_to_draw):
#useful for identifying which variables are possible to be pulled out for scaling or different distributions, despite appearing like arbitrary abstractions
c = 1 #used to vary sample size by a scalar multiplier
alpha = 1 #30 #prior
beta = 1 #70 #prior
views = pool * c
clicks = events * c
return beta_dist(clicks + alpha, views - clicks + beta, samples_to_draw)
def sample(self, data=None, n=1):
"""Return n samples from distribution"""
if data is None:
data = self.data
successes = count_nonzero(data)
total = len(data)
samples = beta_dist(self.alpha + successes,
self.beta + total - successes, n)
return samples
def p_donate_ci(self, a=5, alpha =1, beta=1):
"""
Rretuns a 100-a credible interval
for the donation rate
"""
ones = self.counts[1:]
zeros = self.counts[0]
dist = beta_dist(ones + alpha, zeros + beta, 10000)
lower_bound = np.percentile(dist, a / 2.0)
upper_bound = np.percentile(dist, 100 - a / 2.0)
mean = np.mean(dist)
return (lower_bound, self.p_donate, upper_bound)
def calculate_clickthrough_prob(clicks_A, views_A, clicks_B, views_B):
'''
INPUT: INT, INT, INT, INT
OUTPUT: FLOAT
Calculate and return an estimated probability that SiteA performs better
(has a higher click-through rate) than SiteB.
Hint: Use Bayesian A/B Testing (multi-armed-bandit repo)
'''
samp = 10000
Aa = clicks_A + 1
Ab = clicks_B + 1
Ba = views_A - clicks_A + 1
Bb = views_B - clicks_B + 1
A_prob = beta_dist(Aa, Ba, samp)
B_prob = beta_dist(Ab, Bb, samp)
return np.sum(A_prob > B_prob) / float(samp)
def p_donate_ci(self, a=5, alpha=1, beta=1):
"""
Rretuns a 100-a credible interval
for the donation rate
"""
ones = self.counts[1:]
zeros = self.counts[0]
dist = beta_dist(ones + alpha, zeros + beta, 10000)
lower_bound = np.percentile(dist, a / 2.0)
upper_bound = np.percentile(dist, 100 - a / 2.0)
mean = np.mean(dist)
return (lower_bound, self.p_donate, upper_bound)
def _sampled_based(vuln_function, gmf_set, epsilon_provider, asset):
"""Compute the set of loss ratios when at least one CV
(Coefficent of Variation) defined in the vulnerability function
is greater than zero.
:param vuln_function: the vulnerability function used to
compute the loss ratios.
:type vuln_function: :py:class:`openquake.shapes.VulnerabilityFunction`
:param gmf_set: ground motion fields used to compute the loss ratios
:type gmf_set: :py:class:`dict` with the following
keys:
**IMLs** - tuple of ground motion fields (float)
**TimeSpan** - time span parameter (float)
**TSES** - time representative of the Stochastic Event Set (float)
:param epsilon_provider: service used to get the epsilon when
using the sampled based algorithm.
:type epsilon_provider: object that defines an :py:meth:`epsilon` method
:param asset: the asset used to compute the loss ratios.
:type asset: an :py:class:`openquake.db.model.ExposureData` instance
"""
loss_ratios = []
for ground_motion_field in gmf_set["IMLs"]:
if ground_motion_field < vuln_function.imls[0]:
loss_ratios.append(0.0)
else:
if ground_motion_field > vuln_function.imls[-1]:
ground_motion_field = vuln_function.imls[-1]
mean_ratio = vuln_function.loss_ratio_for(ground_motion_field)
cov = vuln_function.cov_for(ground_motion_field)
if vuln_function.is_beta:
stddev = cov * mean_ratio
alpha = compute_alpha(mean_ratio, stddev)
beta = compute_beta(mean_ratio, stddev)
loss_ratios.append(beta_dist(alpha, beta, size=None))
else:
variance = (mean_ratio * cov) ** 2.0
epsilon = epsilon_provider.epsilon(asset)
sigma = math.sqrt(
math.log((variance / mean_ratio ** 2.0) + 1.0))
mu = math.log(mean_ratio ** 2.0 / math.sqrt(
variance + mean_ratio ** 2.0))
loss_ratios.append(math.exp(mu + (epsilon * sigma)))
return array(loss_ratios)
def __init__(self, alpha: float, beta: float, labels_1: Set[str], labels_2: Set[str], equalities: Mapping,
threshold: float = 0.):
"""
:param alpha: alpha value for beta distribution
:param beta: beta value for beta distribution
:param labels_1: source space
:param labels_2: target space
:param equalities: labels that are considered equal (1 - beta)
:param threshold: every similarity below is considered to be zero
"""
s = ((a, b, beta_dist(alpha, beta)) for a, b in product(labels_1, labels_2))
s = ((a, b, 1 - w if (a, b) in equalities else w) for a, b, w in s)
s = ((a, b, w if w > threshold else 0.) for a, b, w in s)
super().__init__(s)
def _sampled_based(vuln_function, gmf_set, epsilon_provider, asset):
"""Compute the set of loss ratios when at least one CV
(Coefficent of Variation) defined in the vulnerability function
is greater than zero.
:param vuln_function: the vulnerability function used to
compute the loss ratios.
:type vuln_function: :py:class:`openquake.shapes.VulnerabilityFunction`
:param gmf_set: ground motion fields used to compute the loss ratios
:type gmf_set: :py:class:`dict` with the following
keys:
**IMLs** - tuple of ground motion fields (float)
**TimeSpan** - time span parameter (float)
**TSES** - time representative of the Stochastic Event Set (float)
:param epsilon_provider: service used to get the epsilon when
using the sampled based algorithm.
:type epsilon_provider: object that defines an :py:meth:`epsilon` method
:param asset: the asset used to compute the loss ratios.
:type asset: an :py:class:`openquake.db.model.ExposureData` instance
"""
loss_ratios = []
for ground_motion_field in gmf_set["IMLs"]:
if ground_motion_field < vuln_function.imls[0]:
loss_ratios.append(0.0)
else:
if ground_motion_field > vuln_function.imls[-1]:
ground_motion_field = vuln_function.imls[-1]
mean_ratio = vuln_function.loss_ratio_for(ground_motion_field)
cov = vuln_function.cov_for(ground_motion_field)
if vuln_function.is_beta:
stddev = cov * mean_ratio
alpha = compute_alpha(mean_ratio, stddev)
beta = compute_beta(mean_ratio, stddev)
loss_ratios.append(beta_dist(alpha, beta, size=None))
else:
variance = (mean_ratio * cov)**2.0
epsilon = epsilon_provider.epsilon(asset)
sigma = math.sqrt(math.log((variance / mean_ratio**2.0) + 1.0))
mu = math.log(mean_ratio**2.0 /
math.sqrt(variance + mean_ratio**2.0))
loss_ratios.append(math.exp(mu + (epsilon * sigma)))
return array(loss_ratios)
def sampleSuccessRateForBinomialDataAndBetaPriori(data_n,data_k,alpha=1,beta=1,samples=10000):
return beta_dist(data_k+alpha, data_n-data_k+beta, samples)
from numpy.random import beta as beta_dist
from numpy import percentile
import numpy as np
N_samp = 10000000 # number of samples to draw
c = 1 #used to vary sample size by a scalar multiplier
## INSERT YOUR OWN DATA HERE
clicks_A = (44) * c
views_A = (9610) * c
clicks_B = (426) * c
views_B = (83617) * c
alpha = 1 #30 #prior
beta = 1 #70 #prior
A_samples = beta_dist(clicks_A + alpha, views_A - clicks_A + beta, N_samp)
B_samples = beta_dist(clicks_B + alpha, views_B - clicks_B + beta, N_samp)
#confidence intervals: eg 2.5 = 95, 10 = 80
print[
round(np.percentile((B_samples - A_samples) / B_samples, 2.5), 4),
round(np.percentile((B_samples - A_samples) / B_samples, 97.5), 4)
]
print[
round(np.percentile((B_samples - A_samples) / B_samples, 10), 4),
round(np.percentile((B_samples - A_samples) / B_samples, 90), 4)
]
# percent lift needed
# base lift 1,
'''
v_conversions = 1799 * c
v_visits = 207434 * c
#lift_perc = .03
c_mean = 80.03
c_var = 503950.69
v_mean = 78.64
v_var = 493547.51
N_samp = 75000
clicks_A = c_conversions
views_A = c_visits
clicks_B = v_conversions
views_B = v_visits
alpha = 1
beta = 1
A_conv_samps = beta_dist(clicks_A + alpha, views_A - clicks_A + beta, N_samp)
B_conv_samps = beta_dist(clicks_B + alpha, views_B - clicks_B + beta, N_samp)
A_order_samps = draw_mus(c_conversions, c_mean, c_var, 0, 1, 1, 1, N_samp)
B_order_samps = draw_mus(v_conversions, v_mean, v_var, 0, 1, 1, 1, N_samp)
A_rps_samps = A_conv_samps * A_order_samps
B_rps_samps = B_conv_samps * B_order_samps
# set current winner
if (mean(A_rps_samps) >= mean(B_rps_samps)):
Current_Winner_rps_samps = A_rps_samps
Current_Loser_rps_samps = B_rps_samps
current_winner_str = "CHOOSE CONTROL"
else:
Current_Winner_rps_samps = B_rps_samps
def get_samples(success, population, alpha, beta, sample_size):
return beta_dist(success+alpha, population-success+beta, sample_size)
A_log_norm_data = lognormal(mean=4.20, sigma=1.0, size=100) B_log_norm_data = lognormal(mean=4.00, sigma=1.0, size=100) # appending many many zeros A_data = concatenate([A_log_norm_data,zeros((10000))]) B_data = concatenate([B_log_norm_data,zeros((10000))]) # modeling zero vs. non-zero non_zeros_A = sum(A_data > 0) total_A = len(A_data) non_zeros_B = sum(B_data > 0) total_B = len(B_data) alpha = 1 # uniform prior beta = 1 n_samples = 100000 # number of samples to draw A_conv_samps = beta_dist(non_zeros_A+alpha, total_A-non_zeros_A+beta, n_samples) B_conv_samps = beta_dist(non_zeros_B+alpha, total_B-non_zeros_B+beta, n_samples) # modeling the non-zeros with a log-normal A_non_zero_data = A_data[A_data > 0] B_non_zero_data = B_data[B_data > 0] m0 = 4. k0 = 1. s_sq0 = 1. v0 = 1. A_order_samps = draw_log_normal_means(A_non_zero_data,m0,k0,s_sq0,v0,n_samples) B_order_samps = draw_log_normal_means(B_non_zero_data,m0,k0,s_sq0,v0,n_samples) # combining the two
def init_user(self, graph):
dist = beta_dist(self.alpha, self.beta, len(graph._workers._nodes))
for i, (worker, _, _, _, _) in enumerate(graph.workers()):
worker.p = dist[i]
def init_user(self, graph):
dist = beta_dist(self.alpha, self.beta, len(graph._workers._nodes))
for i, (worker, _, _, _, _) in enumerate(graph.workers()):
worker.p = dist[i]
def get_samples(success, population, alpha, beta, sample_size):
return beta_dist(success + alpha, population - success + beta, sample_size)