def test_conditional_simple():
A = np.ones((1,2))
b = np.array([1])
con = AC.constraints(A,b) #X1+X2<= 1
C = np.array([[0,1]])
d = np.array([2]) #X2=2
new_con = con.conditional(C,d)
while True:
W = np.random.standard_normal(2)
W -= np.dot(np.linalg.pinv(C), np.dot(C, W) - d)
if con(W):
break
Z1 = AC.sample_from_constraints(new_con, W, ndraw=10000)
counter = 0
new_sample = []
while True:
W = np.random.standard_normal() # conditional distribution
if W < -1:
new_sample.append(W)
counter += 1
if counter >= 10000:
break
a1 = Z1[:,0]
a2 = np.array(new_sample)
test = np.fabs((a1.mean() - a2.mean()) / (np.std(a1) * np.sqrt(2)) * np.sqrt(10000))
nt.assert_true(test < 5)
def test_conditional():
p = 200
k1, k2 = 5, 3
b = np.random.standard_normal((k1,))
A = np.random.standard_normal((k1,p))
con = AC.constraints(A,b)
w = np.random.standard_normal(p)
con.mean = w
C = np.random.standard_normal((k2,p))
d = np.random.standard_normal(k2)
new_con = con.conditional(C, d)
while True:
W = np.random.standard_normal(p)
W -= np.dot(np.linalg.pinv(C), np.dot(C, W) - d)
if new_con(W) and con(W):
break
Z = AC.sample_from_constraints(new_con, W, ndraw=5000)
tol = 0
nt.assert_true(np.linalg.norm(np.dot(Z, C.T) - d[None,:]) < 1.e-7)
V = (np.dot(Z, new_con.linear_part.T) - new_con.offset[None,:]).max(1)
V2 = (np.dot(Z, con.linear_part.T) - con.offset[None,:]).max(1)
print ('failing:',
(V>tol).sum(),
(V2>tol).sum(),
np.linalg.norm(np.dot(C, W) - d))
nt.assert_true(np.sum(V > tol) < 0.001*V.shape[0])
def test_conditional():
p = 200
k1, k2 = 5, 3
b = np.random.standard_normal((k1,))
A = np.random.standard_normal((k1,p))
con = AC.constraints(A,b)
w = np.random.standard_normal(p)
con.mean = w
C = np.random.standard_normal((k2,p))
d = np.random.standard_normal(k2)
new_con = con.conditional(C, d)
while True:
W = np.random.standard_normal(p)
W -= np.dot(np.linalg.pinv(C), np.dot(C, W) - d)
if new_con(W) and con(W):
break
Z = AC.sample_from_constraints(new_con, W, ndraw=5000)
tol = 0
nt.assert_true(np.linalg.norm(np.dot(Z, C.T) - d[None,:]) < 1.e-7)
V = (np.dot(Z, new_con.linear_part.T) - new_con.offset[None,:]).max(1)
V2 = (np.dot(Z, con.linear_part.T) - con.offset[None,:]).max(1)
print ('failing:',
(V>tol).sum(),
(V2>tol).sum(),
np.linalg.norm(np.dot(C, W) - d))
nt.assert_true(np.sum(V > tol) < 0.001*V.shape[0])
def test_conditional_simple():
A = np.ones((1,2))
b = np.array([1])
con = AC.constraints(A,b) #X1+X2<= 1
C = np.array([[0,1]])
d = np.array([2]) #X2=2
new_con = con.conditional(C,d)
while True:
W = np.random.standard_normal(2)
W -= np.dot(np.linalg.pinv(C), np.dot(C, W) - d)
if con(W):
break
Z1 = AC.sample_from_constraints(new_con, W, ndraw=10000)
counter = 0
new_sample = []
while True:
W = np.random.standard_normal() # conditional distribution
if W < -1:
new_sample.append(W)
counter += 1
if counter >= 10000:
break
a1 = Z1[:,0]
a2 = np.array(new_sample)
test = np.fabs((a1.mean() - a2.mean()) / (np.std(a1) * np.sqrt(2)) * np.sqrt(10000))
nt.assert_true(test < 5)
def power(n, snr, pos, rho=0.25,
muval = np.linspace(0,5,51)):
X, mu, beta = parameters(n, rho, pos)
# form the correct constraints
con, initial = constraints(X, pos)
Z_selection = sample_from_constraints(con, initial, ndraw=4000000, burnin=100000)
S0 = np.dot(X.T, Z_selection.T).T
W0 = np.ones(S0.shape[0])
dfam0 = discrete_family(S0[:,pos], W0)
one_sided_acceptance_region = dfam0.one_sided_acceptance(0)
def one_sided_power(mu):
L, U = one_sided_acceptance_region
return 1 - (dfam0.cdf(mu,U) - dfam0.cdf(mu, L))
power_fig = plt.figure(figsize=(8,8))
power_ax = power_fig.gca()
power_ax.set_ylabel('Power', fontsize=20)
power_ax.legend(loc='lower right')
power_ax.set_xlabel('Effect size $\mu$', fontsize=20)
full_power = np.array([one_sided_power(m) for m in muval])
print full_power
power_ax.plot(muval, full_power, label='Reduced model UMPU', linewidth=7, alpha=0.5)
power_ax.legend(loc='lower right')
power_ax.set_xlim([0,5])
power_ax.plot([snr,snr],[0,1], 'k--')
print one_sided_power(snr)
return power_fig, {'full':full_power}
def simulation(n, snr, pos, rho=0.25, ndraw=5000, burnin=1000):
X, mu, beta = parameters(n, rho, pos)
con, initial = constraints(X, pos)
con.mean = snr * mu / np.sqrt(2)
Z_selection = sample_from_constraints(con, initial, ndraw=ndraw, burnin=burnin)
Z_inference_pos = np.random.standard_normal(Z_selection.shape[0]) + snr / np.sqrt(2)
return (np.dot(X.T, Z_selection.T)[pos] + Z_inference_pos) / np.sqrt(2)
def power(mu, ndraw=100000, keep_every=100):
constraint = affine.constraints(np.array([[-1,0.]]), np.array([-cutoff]))
constraint.mean = np.array([mu,mu])
sample = affine.sample_from_constraints(constraint, np.array([4,2.]),
ndraw=ndraw)[::keep_every]
print sample.mean(0)
sample = sample.sum(1)
decisions = []
for s in sample:
decisions.append(null_dbn.one_sided_test(0, s, alternative='greater'))
print np.mean(decisions)
return np.mean(decisions)
def simulation(n, snr, pos, rho=0.25, ndraw=5000, burnin=1000):
X, mu, beta = parameters(n, rho, pos)
con, initial = constraints(X, pos)
con.mean = snr * mu / np.sqrt(2)
Z_selection = sample_from_constraints(con,
initial,
ndraw=ndraw,
burnin=burnin)
Z_inference_pos = np.random.standard_normal(
Z_selection.shape[0]) + snr / np.sqrt(2)
return (np.dot(X.T, Z_selection.T)[pos] + Z_inference_pos) / np.sqrt(2)
def power(mu, ndraw=100000, keep_every=100):
constraint = affine.constraints(np.array([[-1, 0.]]), np.array([-cutoff]))
constraint.mean = np.array([mu, mu])
sample = affine.sample_from_constraints(constraint,
np.array([4, 2.]),
ndraw=ndraw)[::keep_every]
print sample.mean(0)
sample = sample.sum(1)
decisions = []
for s in sample:
decisions.append(null_dbn.one_sided_test(0, s, alternative='greater'))
print np.mean(decisions)
return np.mean(decisions)
def test_sampling():
"""
See that means and covariances are approximately correct
"""
C = AC.constraints(np.identity(3), np.inf*np.ones(3))
C.mean = np.array([3,4,5.2])
W = np.random.standard_normal((5,3))
S = np.dot(W.T, W) / 30.
C.covariance = S
V = AC.sample_from_constraints(C, np.zeros(3), ndraw=500000)
nt.assert_true(np.linalg.norm(V.mean(0)-C.mean) < 0.01)
nt.assert_true(np.linalg.norm(np.einsum('ij,ik->ijk', V, V).mean(0) -
np.outer(V.mean(0), V.mean(0)) - S) < 0.01)
def cone_with_slice(angles,
ai,
hull,
which,
fill_args={},
ax=None,
label=None,
suffix='',
Y=None):
ax, poly, constraint, rays = cone_rays(angles,
ai,
hull,
which,
ax=ax,
fill_args=fill_args)
eta_idx = np.argmax(np.dot(hull.points, Y))
eta = 40 * hull.points[eta_idx]
representation = constraints(-constraint.T, np.zeros(2))
if Y is None:
Y = sample_from_constraints(representation)
ax.fill(poly[:, 0], poly[:, 1], label=r'$A_{(M,H_0)}$', **fill_args)
if symmetric:
ax.fill(-poly[:, 0], -poly[:, 1], **fill_args)
legend_args = {'scatterpoints': 1, 'fontsize': 30, 'loc': 'lower left'}
ax.legend(**legend_args)
ax.figure.savefig('fig_onesparse1.png', dpi=300)
ax.scatter(Y[0], Y[1], c='k', s=150, label=label)
Vp, _, Vm = representation.bounds(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) / np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp * eta / np.linalg.norm(eta)**2),
(Yperp + Vm * eta / np.linalg.norm(eta)**2)])
ax.plot(width_points[:, 0], width_points[:, 1], '-', c='k', linewidth=4)
legend_args = {'scatterpoints': 1, 'fontsize': 30, 'loc': 'lower left'}
ax.legend(**legend_args)
ax.figure.savefig('fig_onesparse2.png', dpi=300)
return ax, poly, constraint, rays
def test_sampling():
"""
See that means and covariances are approximately correct
"""
C = AC.constraints(np.identity(3), np.inf*np.ones(3))
C.mean = np.array([3,4,5.2])
W = np.random.standard_normal((5,3))
S = np.dot(W.T, W) / 30.
C.covariance = S
V = AC.sample_from_constraints(C, np.zeros(3), ndraw=500000)
nt.assert_true(np.linalg.norm(V.mean(0)-C.mean) < 0.01)
nt.assert_true(np.linalg.norm(np.einsum('ij,ik->ijk', V, V).mean(0) -
np.outer(V.mean(0), V.mean(0)) - S) < 0.01)
def test_simulate_nonwhitened():
n, p = 50, 200
X = np.random.standard_normal((n,p))
cov = np.dot(X.T, X)
W = np.random.standard_normal((3,p))
con = AC.constraints(W, np.ones(3), covariance=cov)
while True:
z = np.random.standard_normal(p)
if np.dot(W, z).max() <= 1:
break
Z = AC.sample_from_constraints(con, z)
nt.assert_true((np.dot(Z, W.T) - 1).max() < 0)
def test_simulate_nonwhitened():
n, p = 50, 200
X = np.random.standard_normal((n,p))
cov = np.dot(X.T, X)
W = np.random.standard_normal((3,p))
con = AC.constraints(W, np.ones(3), covariance=cov)
while True:
z = np.random.standard_normal(p)
if np.dot(W, z).max() <= 1:
break
Z = AC.sample_from_constraints(con, z)
nt.assert_true((np.dot(Z, W.T) - 1).max() < 0)
def draw_sample(mu, cutoff, nsample=10000):
if mu >= cutoff - 4:
sample = []
while True:
candidate = np.random.standard_normal(1000000) + mu
candidate = candidate[candidate > cutoff]
sample.extend(candidate)
if len(sample) > nsample:
break
sample = np.array(sample)
sample += np.random.standard_normal(sample.shape) + mu
else:
constraint = affine.constraints(np.array([[-1,0.]]), np.array([-cutoff]))
constraint.mean = np.array([mu,mu])
sample = affine.sample_from_constraints(constraint, np.array([cutoff + 0.1,0]),
ndraw=2000000,
direction_of_interest=np.array([1,1.]))
sample = sample.sum(1)[::(2000000/nsample)]
return sample
def cone_with_slice(angles, ai, hull, which, fill_args={}, ax=None, label=None,
suffix='',
Y=None):
ax, poly, constraint, rays = cone_rays(angles, ai, hull, which, ax=ax, fill_args=fill_args)
eta_idx = np.argmax(np.dot(hull.points, Y))
eta = 40 * hull.points[eta_idx]
representation = constraints(-constraint.T, np.zeros(2))
if Y is None:
Y = sample_from_constraints(representation)
ax.fill(poly[:,0], poly[:,1], label=r'$A_{(M,H_0)}$', **fill_args)
if symmetric:
ax.fill(-poly[:,0], -poly[:,1], **fill_args)
legend_args = {'scatterpoints':1, 'fontsize':30, 'loc':'lower left'}
ax.legend(**legend_args)
ax.figure.savefig('fig_onesparse1.png', dpi=300)
ax.scatter(Y[0], Y[1], c='k', s=150, label=label)
Vp, _, Vm = representation.bounds(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) /
np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp*eta /
np.linalg.norm(eta)**2),
(Yperp + Vm*eta /
np.linalg.norm(eta)**2)])
ax.plot(width_points[:,0], width_points[:,1], '-', c='k', linewidth=4)
legend_args = {'scatterpoints':1, 'fontsize':30, 'loc':'lower left'}
ax.legend(**legend_args)
ax.figure.savefig('fig_onesparse2.png', dpi=300)
return ax, poly, constraint, rays
def test_pivots_intervals():
A, b = np.random.standard_normal((4,30)), np.random.standard_normal(4)
con = AC.constraints(A,b)
while True:
w = np.random.standard_normal(30)
if con(w):
break
Z = AC.sample_from_constraints(con, w)[-1]
u = np.zeros(con.dim)
u[4] = 1
# call pivot
con.pivot(u, Z)
con.pivot(u, Z, alternative='less')
con.pivot(u, Z, alternative='greater')
con.interval(u, Z, UMAU=True)
con.interval(u, Z, UMAU=False)
def test_pivots_intervals():
A, b = np.random.standard_normal((4,30)), np.random.standard_normal(4)
con = AC.constraints(A,b)
while True:
w = np.random.standard_normal(30)
if con(w):
break
Z = AC.sample_from_constraints(con, w)[-1]
u = np.zeros(con.dim)
u[4] = 1
# call pivot
con.pivot(u, Z)
con.pivot(u, Z, alternative='less')
con.pivot(u, Z, alternative='greater')
con.interval(u, Z, UMAU=True)
con.interval(u, Z, UMAU=False)
def power(n, snr, pos, rho=0.25, muval=np.linspace(0, 5, 51)):
X, mu, beta = parameters(n, rho, pos)
# form the correct constraints
con, initial = constraints(X, pos)
Z_selection = sample_from_constraints(con,
initial,
ndraw=4000000,
burnin=100000)
S0 = np.dot(X.T, Z_selection.T).T
W0 = np.ones(S0.shape[0])
dfam0 = discrete_family(S0[:, pos], W0)
one_sided_acceptance_region = dfam0.one_sided_acceptance(0)
def one_sided_power(mu):
L, U = one_sided_acceptance_region
return 1 - (dfam0.cdf(mu, U) - dfam0.cdf(mu, L))
power_fig = plt.figure(figsize=(8, 8))
power_ax = power_fig.gca()
power_ax.set_ylabel('Power', fontsize=20)
power_ax.legend(loc='lower right')
power_ax.set_xlabel('Effect size $\mu$', fontsize=20)
full_power = np.array([one_sided_power(m) for m in muval])
print full_power
power_ax.plot(muval,
full_power,
label='Reduced model UMPU',
linewidth=7,
alpha=0.5)
power_ax.legend(loc='lower right')
power_ax.set_xlim([0, 5])
power_ax.plot([snr, snr], [0, 1], 'k--')
print one_sided_power(snr)
return power_fig, {'full': full_power}
def test_chisq_central():
n, p = 4, 10
A, b = np.random.standard_normal((n, p)), np.zeros(n)
con = AC.constraints(A,b)
while True:
z = np.random.standard_normal(p)
if con(z):
break
S = np.identity(p)[:3]
Z = AC.sample_from_constraints(con, z, ndraw=10000)
P = []
for i in range(Z.shape[0]/10):
P.append(chisq.quadratic_test(Z[10*i], S, con))
ecdf = sm.distributions.ECDF(P)
plt.clf()
x = np.linspace(0,1,101)
plt.plot(x, ecdf(x), c='red')
plt.plot([0,1],[0,1], c='blue', linewidth=2)
nt.assert_true(np.fabs(np.mean(P)-0.5) < 0.03)
nt.assert_true(np.fabs(np.std(P)-1/np.sqrt(12)) < 0.03)
def test_chisq_central():
n, p = 4, 10
A, b = np.random.standard_normal((n, p)), np.zeros(n)
con = AC.constraints(A, b)
while True:
z = np.random.standard_normal(p)
if con(z):
break
S = np.identity(p)[:3]
Z = AC.sample_from_constraints(con, z, ndraw=10000)
P = []
for i in range(Z.shape[0] / 10):
P.append(chisq.quadratic_test(Z[10 * i], S, con))
ecdf = sm.distributions.ECDF(P)
plt.clf()
x = np.linspace(0, 1, 101)
plt.plot(x, ecdf(x), c='red')
plt.plot([0, 1], [0, 1], c='blue', linewidth=2)
nt.assert_true(np.fabs(np.mean(P) - 0.5) < 0.03)
nt.assert_true(np.fabs(np.std(P) - 1 / np.sqrt(12)) < 0.03)
import os
import numpy as np
import matplotlib.pyplot as plt
from selection import affine
from selection.discrete_family import discrete_family
from scipy.stats import norm as ndist
cutoff = ndist.ppf(0.95)
null_constraint = affine.constraints(np.array([[-1, 0.]]), np.array([-cutoff]))
null_sample = affine.sample_from_constraints(null_constraint,
np.array([4, 2.]),
ndraw=100000).sum(1)
null_dbn = discrete_family(null_sample, np.ones_like(null_sample))
def power(mu, ndraw=100000, keep_every=100):
constraint = affine.constraints(np.array([[-1, 0.]]), np.array([-cutoff]))
constraint.mean = np.array([mu, mu])
sample = affine.sample_from_constraints(constraint,
np.array([4, 2.]),
ndraw=ndraw)[::keep_every]
print sample.mean(0)
sample = sample.sum(1)
decisions = []
for s in sample:
decisions.append(null_dbn.one_sided_test(0, s, alternative='greater'))
print np.mean(decisions)
return np.mean(decisions)
def marginal(n, snr, pos, rho=0.25, ndraw=5000,
burnin=1000, nsim=5000, sigma=1.):
X, mu, beta = parameters(n, rho, pos)
Psplit = []
Pselect = []
hypotheses = []
for _ in range(nsim):
Y_select = (snr * mu / np.sqrt(2) + np.random.standard_normal(n)) * sigma
con, _, select_pos, sign = covtest(X, Y_select, sigma=sigma, exact=True)
cond_ncp = snr * np.dot(X.T[select_pos], mu) / np.sqrt(2) * sign
correct = (sign == +1) and (pos == select_pos)
hypotheses.append(correct)
Y_null = sample_from_constraints(con, Y_select, ndraw=ndraw, burnin=burnin)
Z_null = (np.dot(X.T[select_pos], Y_null.T) + sigma * np.random.standard_normal(ndraw)) / np.sqrt(2)
Z_inference = sigma * (cond_ncp + np.random.standard_normal())
Z_observed = (np.dot(X.T[select_pos], Y_select) * sign + Z_inference) / np.sqrt(2)
dfam = discrete_family(Z_null, np.ones(Z_null.shape))
Pselect.append(dfam.ccdf(0, Z_observed))
if sign == +1:
Psplit.append(ndist.sf(Z_inference / sigma))
else:
Psplit.append(ndist.cdf(Z_inference / sigma))
Ugrid = np.linspace(0,1,101)
Psplit = np.array(Psplit)
Pselect = np.array(Pselect)
hypotheses = np.array(hypotheses, np.bool)
# plot of marginal distribution of p-values
fig1 = plt.figure(figsize=(8,8))
ax1 = fig1.gca()
ax1.plot(Ugrid, ECDF(Psplit)(Ugrid), label='Sample splitting', c='red', linewidth=5, alpha=0.5)
ax1.plot(Ugrid, ECDF(Pselect)(Ugrid), label='Selected using $i^*(Z_S)$', c='blue', linewidth=5, alpha=0.5)
ax1.set_xlabel('P-value, $p$', fontsize=20)
ax1.set_ylabel('ECDF($p$)', fontsize=20)
ax1.plot([0.05,0.05],[0,1], 'k--')
ax1.legend(loc='lower right')
# conditional distribution of p-values
# conditioned on selection choosing correct position and sign
fig2 = plt.figure(figsize=(8,8))
ax2 = fig2.gca()
ax2.plot(Ugrid, ECDF(Psplit[hypotheses])(Ugrid), label='Sample splitting', c='red', linewidth=5, alpha=0.5)
ax2.plot(Ugrid, ECDF(Pselect[hypotheses])(Ugrid), label='Selected using $i^*(Z_S)$', c='blue', linewidth=5, alpha=0.5)
ax2.set_xlabel('P-value, $p$', fontsize=20)
ax2.set_ylabel('ECDF($p$)', fontsize=20)
ax2.plot([0.05,0.05],[0,1], 'k--')
ax2.legend(loc='lower right')
dbn1 = {}
dbn1['split'] = Psplit
dbn1['select'] = Pselect
dbn1['hypotheses'] = hypotheses
return fig1, fig2, dbn1
def marginal(n,
snr,
pos,
rho=0.25,
ndraw=5000,
burnin=1000,
nsim=5000,
sigma=1.):
X, mu, beta = parameters(n, rho, pos)
Psplit = []
Pselect = []
hypotheses = []
for _ in range(nsim):
Y_select = (snr * mu / np.sqrt(2) +
np.random.standard_normal(n)) * sigma
con, _, select_pos, sign = covtest(X,
Y_select,
sigma=sigma,
exact=True)
cond_ncp = snr * np.dot(X.T[select_pos], mu) / np.sqrt(2) * sign
correct = (sign == +1) and (pos == select_pos)
hypotheses.append(correct)
Y_null = sample_from_constraints(con,
Y_select,
ndraw=ndraw,
burnin=burnin)
Z_null = (np.dot(X.T[select_pos], Y_null.T) +
sigma * np.random.standard_normal(ndraw)) / np.sqrt(2)
Z_inference = sigma * (cond_ncp + np.random.standard_normal())
Z_observed = (np.dot(X.T[select_pos], Y_select) * sign +
Z_inference) / np.sqrt(2)
dfam = discrete_family(Z_null, np.ones(Z_null.shape))
Pselect.append(dfam.ccdf(0, Z_observed))
if sign == +1:
Psplit.append(ndist.sf(Z_inference / sigma))
else:
Psplit.append(ndist.cdf(Z_inference / sigma))
Ugrid = np.linspace(0, 1, 101)
Psplit = np.array(Psplit)
Pselect = np.array(Pselect)
hypotheses = np.array(hypotheses, np.bool)
# plot of marginal distribution of p-values
fig1 = plt.figure(figsize=(8, 8))
ax1 = fig1.gca()
ax1.plot(Ugrid,
ECDF(Psplit)(Ugrid),
label='Sample splitting',
c='red',
linewidth=5,
alpha=0.5)
ax1.plot(Ugrid,
ECDF(Pselect)(Ugrid),
label='Selected using $i^*(Z_S)$',
c='blue',
linewidth=5,
alpha=0.5)
ax1.set_xlabel('P-value, $p$', fontsize=20)
ax1.set_ylabel('ECDF($p$)', fontsize=20)
ax1.plot([0.05, 0.05], [0, 1], 'k--')
ax1.legend(loc='lower right')
# conditional distribution of p-values
# conditioned on selection choosing correct position and sign
fig2 = plt.figure(figsize=(8, 8))
ax2 = fig2.gca()
ax2.plot(Ugrid,
ECDF(Psplit[hypotheses])(Ugrid),
label='Sample splitting',
c='red',
linewidth=5,
alpha=0.5)
ax2.plot(Ugrid,
ECDF(Pselect[hypotheses])(Ugrid),
label='Selected using $i^*(Z_S)$',
c='blue',
linewidth=5,
alpha=0.5)
ax2.set_xlabel('P-value, $p$', fontsize=20)
ax2.set_ylabel('ECDF($p$)', fontsize=20)
ax2.plot([0.05, 0.05], [0, 1], 'k--')
ax2.legend(loc='lower right')
dbn1 = {}
dbn1['split'] = Psplit
dbn1['select'] = Pselect
dbn1['hypotheses'] = hypotheses
return fig1, fig2, dbn1
import os
from glob import glob
import numpy as np
import matplotlib.pyplot as plt
from selection import affine
from selection.discrete_family import discrete_family
from scipy.stats import norm as ndist
from sklearn.isotonic import IsotonicRegression
cutoff = 3.
null_constraint = affine.constraints(np.array([[-1,0.]]), np.array([-cutoff]))
null_sample = affine.sample_from_constraints(null_constraint, np.array([4,2.]),
ndraw=100000).sum(1)
null_dbn = discrete_family(null_sample, np.ones_like(null_sample))
def draw_sample(mu, cutoff, nsample=10000):
if mu >= cutoff - 4:
sample = []
while True:
candidate = np.random.standard_normal(1000000) + mu
candidate = candidate[candidate > cutoff]
sample.extend(candidate)
if len(sample) > nsample:
break
sample = np.array(sample)
sample += np.random.standard_normal(sample.shape) + mu
else:
constraint = affine.constraints(np.array([[-1,0.]]), np.array([-cutoff]))
constraint.mean = np.array([mu,mu])
sample = affine.sample_from_constraints(constraint, np.array([cutoff + 0.1,0]),
ndraw=2000000,
