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censorship.py
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import numpy as np
import scipy.special as sp
from scipy.stats import nbinom
p = 0.3
eps_1 = .01
eps_2 = .01
q = 1- p - eps_1-eps_2
k = 3
lamma = 0.001
#### censorship
def table(lamma, p, eps_1, eps_2, k):
a = statsNN(p, eps_1, eps_2, k)
T11 = (a[0]*lamma +a[1], a[2]*lamma + a[3])
a = statsNC(p, eps_1, eps_2, k)
T12 = (a[0]*lamma + a[1], a[2]*lamma + a[3])
a = statsNC(p, eps_2, eps_1, k)
T21 = (a[2]*lamma + a[3], a[0]*lamma + a[1])
a = statsCC(p, eps_1, eps_2, k)
T22 = (a[0]*lamma + a[1], a[2]*lamma + a[3])
return(T11, T12, T21, T22)
def normalized_table(lamma, p, eps_1, eps_2, k):
a = statsNN(p, eps_1, eps_2, k)
T11 = ((a[0]*lamma +a[1])/eps_1, (a[2]*lamma + a[3])/eps_2)
a = statsNC(p, eps_1, eps_2, k)
T12 = ((a[0]*lamma +a[1])/eps_1, (a[2]*lamma + a[3])/eps_2)
a = statsNC(p, eps_2, eps_1, k)
T21 = ((a[2]*lamma +a[3])/eps_1, (a[0]*lamma + a[1])/eps_2)
a = statsCC(p, eps_1, eps_2, k)
T22 = ((a[0]*lamma +a[1])/eps_1, (a[2]*lamma + a[3])/eps_2)
return(T11, T12, T21, T22)
def ntcsv(lamma, p, eps_1, eps_2, k):
B = normalized_table(lamma, p, eps_1, eps_2, k)
df = pd.DataFrame(np.asarray(B))
df.to_csv("table.csv")
import pandas as pd
df = pd.DataFrame(np.asarray(B))
##NN test code
m = p/(1-p)
q = 1- p - eps_1-eps_2
M_0 =np.asarray( [[np.power(m,-1), 1], [np.power(m,k), 1]])
v_1 = np.asarray([1,0])
M_0i = np.linalg.inv(M_0)
[c_1,c_2] = np.matmul(M_0i,v_1)
M_1 = np.asarray( [[1, -1], [-k*np.power(m,k+1), k]])
w_1 = c_1*m+c_2
unique to pool 1
[ct_1,ct_2] = (eps_1/(1-2*p))*np.matmul(M_0i,M_1).dot([c_1,c_2])
e_1 = ct_1*m+c_2-eps_1*c_2/(1-2*p)+eps_1*c_1*m*m/(1-2*p)
E_1NcNcA = eps_1/(1-p)
E_1NcNcB = -(eps_1/(1-p))*w_1/(1-w_1)-e_1/(1-w_1)
#unique to pool 2
[ct_1,ct_2] = (eps_2/(1-2*p))*np.matmul(M_0i,M_1).dot([c_1,c_2])
e_2 = ct_1*m+c_2-eps_2*c_2/(1-2*p)+eps_2*c_1*m*m/(1-2*p)
E_2NcNcA = eps_2/(1-p)
E_2NcNcB = -(eps_2/(1-p))*w_1/(1-w_1)-e_2/(1-w_1)
def statsNN(p, eps_1, eps_2, k):
m = p/(1-p)
q = 1- p - eps_1-eps_2
M_0 =np.asarray( [[np.power(m,-1), 1], [np.power(m,k), 1]])
##NCNC
v_1 = np.asarray([1,0])
M_0i = np.linalg.inv(M_0)
[c_1,c_2] = np.matmul(M_0i,v_1)
M_1 = np.asarray( [[1, -1], [-k*np.power(m,k+1), k]])
w_1 = c_1*m+c_2
#unique to pool 1
[ct1_1,ct1_2] = (eps_1/(1-2*p))*np.matmul(M_0i,M_1).dot([c_1,c_2])
e_1 = ct1_1*m+ct1_2-eps_1*c_2/(1-2*p)+eps_1*c_1*m*m/(1-2*p)
E_1NcNcA = eps_1/(1-p)
E_1NcNcB = -(eps_1/(1-p))*w_1/(1-w_1)-e_1/(1-w_1)
#unique to pool 2
[ct2_1,ct2_2] = (eps_2/(1-2*p))*np.matmul(M_0i,M_1).dot([c_1,c_2])
e_2 = ct2_1*m+ct2_2-eps_2*c_2/(1-2*p)+eps_2*c_1*m*m/(1-2*p)
E_2NcNcA = eps_2/(1-p)
E_2NcNcB = -(eps_2/(1-p))*w_1/(1-w_1)-e_2/(1-w_1)
return(E_1NcNcA,E_1NcNcB,E_2NcNcA,E_2NcNcB)
def statsNC(p, eps_1, eps_2, k):
m = p/(1-p)
q = 1- p - eps_1-eps_2
pt = p+eps_2
M3 = np.asarray( [[1, 1,-1], [m, 1, -1/(1-pt)],[np.power(m,k), 1,0]])
v_3 = np.asarray([0,-pt/(1-pt),0])
M3i = np.linalg.inv(M3)
[c_1,c_2, b] = np.matmul(M3i,v_3)
w_1 = c_1*m+c_2
#Pool1
M4 = np.asarray( [[0, 0,0], [-w_1/(1-pt), -m*m/(1-2*p), 1/(1-2*p)],[0,-k*np.power(m,k+1)/(1-2*p), k/(1-2*p)]])
[ct1_1,ct1_2, b_1] = eps_1*M3i.dot(M4).dot([1,c_1,c_2])
e_1 = (b_1 - eps_1*w_1)/(1-pt)
E_1NcCA = eps_1/(1-pt)
E_1NcCB = -(eps_1/(1-pt))*w_1/(1-w_1)-e_1/(1-w_1)
#Pool2
M4b = np.asarray( [[0, 0], [ -m*m/(1-2*p), 1/(1-2*p)],[-k*np.power(m,k+1)/(1-2*p), k/(1-2*p)]])
[ct2_1,ct2_2, b_2] = eps_2*M3i.dot(M4b).dot([c_1,c_2])
e_2 = b_2/(1-pt)
E_2NcCA = 0
E_2NcCB = -e_2/(1-w_1)
return(E_1NcCA,E_1NcCB,E_2NcCA,E_2NcCB)
def statsCC(p, eps_1, eps_2, k):
m = p/(1-p)
q = 1- p - eps_1-eps_2
pt = p+eps_1+eps_2
M3 = np.asarray( [[1, 1,-1], [m, 1, -1/(1-pt)],[np.power(m,k), 1,0]])
v_3 = np.asarray([0,-pt/(1-pt),0])
M3i = np.linalg.inv(M3)
[c_1,c_2, b] = np.matmul(M3i,v_3)
M4b = np.asarray( [[0, 0], [ -m*m/(1-2*p), 1/(1-2*p)],[-k*np.power(m,k+1)/(1-2*p), k/(1-2*p)]])
w_1 = c_1*m+c_2
#Poo1
[ct1_1,ct1_2, bt_1] = eps_1*M3i.dot(M4b).dot([c_1,c_2])
e_1 = bt_1/(1-pt)
E_1CCA = 0
E_1CCB =-e_1/(1-w_1)
#Poo1 2
[ct2_1,ct2_2, bt_2] = eps_2*M3i.dot(M4b).dot([c_1,c_2])
e_2 = bt_2/(1-pt)
E_2CCA = 0
E_2CCB =-e_2/(1-w_1)
return(E_1CCA,E_1CCB,E_2CCA,E_2CCB)