In [9]:

    

import os
import numpy as np
import pandas as pd
import torch

import matplotlib.pyplot as plt
%matplotlib inline


    

In [51]:

    

torch.manual_seed(20200328)
data = pd.read_csv('data.csv')
device = 'cuda'

n_bootstrap = 100000
repetitions = 10000


    

In [52]:

    

state_black = torch.tensor(data['Fraction Black'].values, device=device)
state_woman = torch.tensor(data['Fraction Female'].values, device=device)


    

In [53]:

    

n_states_2_women = np.empty(n_bootstrap * repetitions, dtype='uint8')
n_black_women = np.empty(n_bootstrap * repetitions, dtype='uint8')
n_black = np.empty(n_bootstrap * repetitions, dtype='uint8')
n_women = np.empty(n_bootstrap * repetitions, dtype='uint8')

for ii in range(repetitions):
    print('{} out of {}'.format(ii, repetitions))
    senate_woman = torch.rand(n_bootstrap, 50, 2, device=device) < state_woman[np.newaxis, :, np.newaxis]
    senate_black = torch.rand(n_bootstrap, 50, 2, device=device) < state_black[np.newaxis, :, np.newaxis]
    both_women_per_state = senate_woman[..., 0] * senate_woman[..., 1]
    n_states_2_women[ii*n_bootstrap:(ii+1)*n_bootstrap] = both_women_per_state.sum(axis=1).cpu().numpy()
    n_black_women[ii*n_bootstrap:(ii+1)*n_bootstrap] = torch.sum(senate_woman * senate_black, dim=(1, 2)).cpu().numpy()
    n_black[ii*n_bootstrap:(ii+1)*n_bootstrap] = senate_black.sum(dim=(1, 2)).cpu().numpy()
    n_women[ii*n_bootstrap:(ii+1)*n_bootstrap] = senate_woman.sum(dim=(1, 2)).cpu().numpy()


    

    




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In [54]:

    

def make_plots(data, reality, description):
    f, axes = plt.subplots(1, 2, figsize=(10, 5))
    for ax in axes:
        h, b, p = ax.hist(data, bins=np.arange(0, 101), density=True)
        ax.plot([reality + .5, reality + .5], [0, 1], c='black')
        ax.set_ylim(h[h>0].min()/10., 1)
        ax.set_xlim(-1, data.max() + 2)
        ax.set_xlabel('Number of {}'.format(description))
        ax.set_ylabel('Probability')
    axes[0].set_ylim(0, .2)
    axes[0].set_yticks([0, .1, .2])
    axes[1].set_yscale('log')
    f.tight_layout()
    print('p for {} or fewer {}: {}'.format(reality, description, np.mean(data <= reality)))
    print('mean for {}: {}'.format(description, data.mean()))
    print('mode for {}: {} at {} probability'.format(description, h.argmax(), h.max()))


    

In [55]:

    

make_plots(n_black_women, 1, 'Black women senators')
plt.savefig(os.path.join(os.environ['HOME'],'Downloads/1BlackWoman.png'), dpi=300)
plt.show()


    

    




p for 1 or fewer Black women senators: 0.027038161
mean for Black women senators: 5.252283138
mode for Black women senators: 5 at 0.183082208 probability






    

In [56]:

    

make_plots(n_black, 3, 'Black senators')
plt.savefig(os.path.join(os.environ['HOME'],'Downloads/3Black.png'), dpi=300)
plt.show()


    

    




p for 3 or fewer Black senators: 0.004893174
mean for Black senators: 10.200075189
mode for Black senators: 10 at 0.138278544 probability






    

In [57]:

    

make_plots(n_states_2_women, 6, 'states with 2 women senators')
plt.savefig(os.path.join(os.environ['HOME'],'Downloads/2WomenStates.png'), dpi=300)
plt.show()


    

    




p for 6 or fewer states with 2 women senators: 0.013464614
mean for states with 2 women senators: 12.977983645
mode for states with 2 women senators: 13 at 0.127745386 probability






    

In [59]:

    

make_plots(n_women, 26, 'women senators')
plt.savefig(os.path.join(os.environ['HOME'],'Downloads/26Women.png'), dpi=300)
plt.show()


    

    




p for 26 or fewer women senators: 3.26e-07
mean for women senators: 50.940140621
mode for women senators: 51 at 0.079605489 probability