def ci_cmle_is(X, v, theta_grid, alpha_level, T = 100, verbose = False):
cmle_is = np.empty_like(theta_grid)
r = X.sum(1)
c = X.sum(0)
for l, theta_l in enumerate(theta_grid):
logit_P_l = theta_l * v
w_l = np.exp(logit_P_l)
z = cond_a_sample(r, c, w_l, T)
logf = np.empty(T)
for t in range(T):
logQ, logP = z[t][1], z[t][2]
logf[t] = logP - logQ
logkappa = -np.log(T) + logsumexp(logf)
if verbose:
logcvsq = -np.log(T - 1) - 2 * logkappa + \
logsumexp(2 * logabsdiffexp(logf, logkappa))
print 'est. cv^2 = %.2f (T = %d)' % (np.exp(logcvsq), T)
cmle_is[l] = np.sum(np.log(w_l[X])) - logkappa
crit = -0.5 * chi2.ppf(1 - alpha_level, 1)
ci = invert_test(theta_grid, cmle_is - cmle_is.max(), crit)
if params['plot']:
plot_statistics(ax_cmle_is, theta_grid, cmle_is - cmle_is.max(), crit)
cmle_is_coverage_data['cis'].append(ci)
cmle_is_coverage_data['theta_grid'] = theta_grid
cmle_is_coverage_data['crit'] = crit
return ci
def ci_cmle_a(X, v, theta_grid, alpha_level):
cmle_a = np.empty_like(theta_grid)
for l, theta_l in enumerate(theta_grid):
logit_P_l = theta_l * v
cmle_a[l] = -cond_a_nll(X, np.exp(logit_P_l))
return invert_test(theta_grid, cmle_a - cmle_a.max(),
-0.5 * chi2.ppf(1 - alpha_level, 1))
def ci_cmle_a(X, v, theta_grid, alpha_level):
cmle_a = np.empty_like(theta_grid)
for l, theta_l in enumerate(theta_grid):
logit_P_l = theta_l * v
cmle_a[l] = -cond_a_nll(X, np.exp(logit_P_l))
return invert_test(theta_grid, cmle_a - cmle_a.max(),
-0.5 * chi2.ppf(1 - alpha_level, 1))
def plot_statistics(ax, theta_grid, test_val, crit):
# Compute confidence interval from test statistics
ci_l, ci_u = invert_test(theta_grid, test_val, crit)
ci_l = max(ci_l, params['theta_l'])
ci_u = min(ci_u, params['theta_u'])
ax.plot(theta_grid, test_val, color = 'b')
ax.hlines(crit, theta_grid[0], theta_grid[-1], linestyle = 'dotted')
ax.hlines(crit, ci_l, ci_u, color = 'r')
ax.vlines(ci_l, 2.0 * crit, crit, color = 'r', linestyle = 'dotted')
ax.vlines(ci_u, 2.0 * crit, crit, color = 'r', linestyle = 'dotted')
ax.set_ylim(2.0 * crit, 0)
def ci_cmle_a(X, v, theta_grid, alpha_level):
cmle_a = np.empty_like(theta_grid)
for l, theta_l in enumerate(theta_grid):
logit_P_l = theta_l * v
cmle_a[l] = -cond_a_nll(X, np.exp(logit_P_l))
crit = -0.5 * chi2.ppf(1 - alpha_level, 1)
ci = invert_test(theta_grid, cmle_a - cmle_a.max(), crit)
if params['plot']:
plot_statistics(ax_cmle_a, theta_grid, cmle_a - cmle_a.max(), crit)
cmle_a_coverage_data['cis'].append(ci)
cmle_a_coverage_data['theta_grid'] = theta_grid
cmle_a_coverage_data['crit'] = crit
return ci
def ci_umle(X, v, theta_grid, alpha_level):
arr = array_from_data(X, [v])
arr.offset_extremes()
alpha_zero(arr)
fit_model = NonstationaryLogistic()
umle = np.empty_like(theta_grid)
for l, theta_l in enumerate(theta_grid):
fit_model.beta['x_0'] = theta_l
fit_model.fit(arr, fix_beta = True)
umle[l] = -fit_model.nll(arr)
crit = -0.5 * chi2.ppf(1 - alpha_level, 1)
ci = invert_test(theta_grid, umle - umle.max(), crit)
if params['plot']:
plot_statistics(ax_umle, theta_grid, umle - umle.max(), crit)
umle_coverage_data['cis'].append(ci)
umle_coverage_data['theta_grid'] = theta_grid
umle_coverage_data['crit'] = crit
return ci
def ci_cmle_is(X, v, theta_grid, alpha_level, T = 100, verbose = False):
cmle_is = np.empty_like(theta_grid)
r = X.sum(1)
c = X.sum(0)
for l, theta_l in enumerate(theta_grid):
logit_P_l = theta_l * v
w_l = np.exp(logit_P_l)
z = cond_a_sample(r, c, w_l, T)
logf = np.empty(T)
for t in range(T):
logQ, logP = z[t][1], z[t][2]
logf[t] = logP - logQ
logkappa = -np.log(T) + logsumexp(logf)
if verbose:
logcvsq = -np.log(T - 1) - 2 * logkappa + \
logsumexp(2 * logabsdiffexp(logf, logkappa))
print 'est. cv^2 = %.2f (T = %d)' % (np.exp(logcvsq), T)
cmle_is[l] = np.sum(np.log(w_l[X])) - logkappa
return invert_test(theta_grid, cmle_is - cmle_is.max(),
-0.5 * chi2.ppf(1 - alpha_level, 1))
def ci_cmle_is(X, v, theta_grid, alpha_level, T=100, verbose=False):
cmle_is = np.empty_like(theta_grid)
r = X.sum(1)
c = X.sum(0)
for l, theta_l in enumerate(theta_grid):
logit_P_l = theta_l * v
w_l = np.exp(logit_P_l)
z = cond_a_sample(r, c, w_l, T)
logf = np.empty(T)
for t in range(T):
logQ, logP = z[t][1], z[t][2]
logf[t] = logP - logQ
logkappa = -np.log(T) + logsumexp(logf)
if verbose:
logcvsq = -np.log(T - 1) - 2 * logkappa + \
logsumexp(2 * logabsdiffexp(logf, logkappa))
print 'est. cv^2 = %.2f (T = %d)' % (np.exp(logcvsq), T)
cmle_is[l] = np.sum(np.log(w_l[X])) - logkappa
return invert_test(theta_grid, cmle_is - cmle_is.max(),
-0.5 * chi2.ppf(1 - alpha_level, 1))