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Bootstrap

Most basic bootstrap demonstrations from personal projects.

Variables to keep in mind:

Inside the bootstrap() function:

  • Bootstrap confidence level (boot_conf)
  • Target statistic (statistic)
  • Number or resamples (n_resamples)
  • Method of bootstrap() (method)

Outside the bootstrap() function:

  • Confidence interval calculation method. Here the Efron method based on percentiles is used. However, exercise caution with it if the data is skewed

Simple bootstrap

import numpy as np  
import pandas as pd  
import matplotlib.pyplot as plt  
from scipy.stats import bootstrap  

data = np.array(df[column])  
  
boot_conf = 0.95  
bootstrap_ci = bootstrap(data=(data, ), statistic=np.mean, confidence_level=boot_conf, random_state=42, n_resamples=1000, method='percentile')  
ci = bootstrap_ci.confidence_interval  

fig, ax = plt.subplots()  
ax.hist(bootstrap_ci.bootstrap_distribution, bins=25)  
ax.axvline(ci[0], color='red', label='Lower: {}'.format(round(ci[0], 2)))  
ax.axvline(ci[1], color='red', label='Upper: {}'.format(round(ci[1], 2)))  
  
ax.set_title('Bootstrap Distribution with {}% CI'.format(round(boot_conf*100)))  
ax.set_xlabel('statistic')  
ax.set_ylabel('frequency')  
  
plt.legend(shadow=True)  
plt.tight_layout()  
plt.show()

image

Bootstrap hypothesis testing

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.stats import bootstrap

data_1 = np.array(df.loc[df[groups] == 1)][column])
data_2 = np.array(df.loc[df[groups] == 2)][column])

boot_conf = 0.95
bootstrap1 = bootstrap(data=(data_1, ), statistic=np.mean, confidence_level=boot_conf, random_state=42, n_resamples=1000, method='percentile')
bootstrap2 = bootstrap(data=(data_2, ), statistic=np.mean, confidence_level=boot_conf, random_state=42, n_resamples=1000, method='percentile')

# Stat difference and Efron's confidence interval
difference = bootstrap2.bootstrap_distribution - bootstrap1.bootstrap_distribution
perc_low = ((1 - boot_conf) / 2) * 100
perc_high = (boot_conf * 100) + perc_low
ci_low = np.percentile(difference, perc_low)
ci_high = np.percentile(difference, perc_high)

# If the distribution is to the right of the red line - bootstrap 2 has bigger values. To the left, the bootstrap2.
fig, ax = plt.subplots()
ax.hist(difference, bins=25)
ax.axvline(x=0, color='red', label='Zero: 0.00')
ax.axvline(ci_low, color='blue', label='Lower: {}'.format(round(ci_low, 2)))
ax.axvline(ci_high, color='blue', label='Upper: {}'.format(round(ci_high, 2)))

ax.set_title('Bootstrap Statistic Difference with {}% CI'.format(round(boot_conf*100)))
ax.set_xlabel('statistic difference')
ax.set_ylabel('frequency')

plt.legend(shadow=True)
plt.tight_layout()
plt.show()

image