def compare_two_samples_from_beta(sample_1, sample_2, significance_level=0.95, plot=True):
""" Compare two samples from Beta distribution """
if plot: hist(sample_1, 100, alpha=0.5); hist(sample_2, 100, alpha=0.5); show()
sample_1_lower_bound, sample_1_upper_bound = get_confidence_intervals_using_the_quantiles(
sample_1, significance_level)
sample_2_lower_bound, sample_2_upper_bound = get_confidence_intervals_using_the_quantiles(
sample_2, significance_level)
if sample_1_lower_bound > sample_2_upper_bound or sample_2_lower_bound > sample_1_upper_bound:
return 'Samples are not equal'
else:
return 'Samples are equal'
def bootstrap_confidence_intervals(a_list_of_values,
bootstrapping_resamples=1000):
""" Bootstrapping confidence intervals """
def sample_wr(population, k):
""" Chooses k random elements (with replacement) from a population """
n = len(population)
_random, _int = random, int
result = [None] * k
for i in xrange(k):
j = _int(_random() * n)
result[i] = population[j]
return result
# Bootstrapping
lower_bounds, upper_bounds = [], []
for _ in range(bootstrapping_resamples):
# create resample with the same size as the original
resample = sample_wr(a_list_of_values, len(a_list_of_values))
# get confidence interval
resample_lower_bound, resample_upper_bound = get_confidence_intervals_using_the_quantiles(
resample)
# append to results
lower_bounds.append(resample_lower_bound)
upper_bounds.append(resample_upper_bound)
mean_lower_bound, mean_upper_bound = mean(lower_bounds), mean(upper_bounds)
return mean_lower_bound, mean_upper_bound
def bootstrap_confidence_intervals(a_list_of_values, bootstrapping_resamples=1000):
""" Bootstrapping confidence intervals """
def sample_wr(population, k):
""" Chooses k random elements (with replacement) from a population """
n = len(population)
_random, _int = random, int
result = [None] * k
for i in xrange(k):
j = _int(_random() * n)
result[i] = population[j]
return result
# Bootstrapping
lower_bounds, upper_bounds = [], []
for _ in range(bootstrapping_resamples):
# create resample with the same size as the original
resample = sample_wr(a_list_of_values, len(a_list_of_values))
# get confidence interval
resample_lower_bound, resample_upper_bound = get_confidence_intervals_using_the_quantiles(resample)
# append to results
lower_bounds.append(resample_lower_bound)
upper_bounds.append(resample_upper_bound)
mean_lower_bound, mean_upper_bound = mean(lower_bounds), mean(upper_bounds)
return mean_lower_bound, mean_upper_bound
def compare_two_samples_from_beta(sample_1,
sample_2,
significance_level=0.95,
plot=True):
""" Compare two samples from Beta distribution """
if plot:
hist(sample_1, 100, alpha=0.5)
hist(sample_2, 100, alpha=0.5)
show()
sample_1_lower_bound, sample_1_upper_bound = get_confidence_intervals_using_the_quantiles(
sample_1, significance_level)
sample_2_lower_bound, sample_2_upper_bound = get_confidence_intervals_using_the_quantiles(
sample_2, significance_level)
if sample_1_lower_bound > sample_2_upper_bound or sample_2_lower_bound > sample_1_upper_bound:
return 'Samples are not equal'
else:
return 'Samples are equal'
def main():
""" BayesianStatistics.py """
data = create_random_sample_from_beta(10, 100, plot=True)
print 'Confidence Interval:', get_confidence_intervals_using_the_quantiles(data)
sample_1 = create_random_sample_from_beta(100, 10000)
sample_2 = create_random_sample_from_beta(100, 10000)
print 'Comparing equal samples:', compare_two_samples_from_beta(sample_1, sample_2)
sample_1 = create_random_sample_from_beta(150, 10000)
sample_2 = create_random_sample_from_beta(100, 10000)
print 'Comparing unequal samples:', compare_two_samples_from_beta(sample_1, sample_2)
def main():
""" BayesianStatistics.py """
data = create_random_sample_from_beta(10, 100, plot=True)
print 'Confidence Interval:', get_confidence_intervals_using_the_quantiles(
data)
sample_1 = create_random_sample_from_beta(100, 10000)
sample_2 = create_random_sample_from_beta(100, 10000)
print 'Comparing equal samples:', compare_two_samples_from_beta(
sample_1, sample_2)
sample_1 = create_random_sample_from_beta(150, 10000)
sample_2 = create_random_sample_from_beta(100, 10000)
print 'Comparing unequal samples:', compare_two_samples_from_beta(
sample_1, sample_2)
