def geweke_test(K, N_iter=10000):
"""
"""
# Create a multinomial distribution
mu = np.zeros(K-1)
mu[-1] = 1
Sigma = np.eye(K-1)
pgm = PGMultinomial(K, mu=mu, Sigma=Sigma)
# Run a Geweke test
xs = []
samples = []
for itr in range(N_iter):
if itr % 10 == 0:
print("Iteration ", itr)
# Resample the data
x = pgm.rvs(10)
# Resample the PG-Multinomial parameters
pgm.resample(x)
# Update our samples
xs.append(x.copy())
samples.append(pgm.copy_sample())
# Check that the PG-Multinomial samples are distributed like the prior
psi_samples = np.array([s.psi for s in samples])
psi_mean = psi_samples.mean(0)
psi_std = psi_samples.std(0)
print("Mean bias: ", psi_mean, " +- ", psi_std)
# Make Q-Q plots
ind = K-2
fig = plt.figure()
ax = fig.add_subplot(121)
psi_dist = norm(mu[ind], np.sqrt(Sigma[ind,ind]))
probplot(psi_samples[:,ind], dist=psi_dist, plot=ax)
fig.add_subplot(122)
_, bins, _ = plt.hist(psi_samples[:,ind], 20, normed=True, alpha=0.2)
bincenters = 0.5*(bins[1:]+bins[:-1])
plt.plot(bincenters, psi_dist.pdf(bincenters), 'r--', linewidth=1)
plt.show()
def test_pgm_rvs():
K = 10
mu, sig = compute_uniform_mean_psi(K, sigma=2)
# mu = np.zeros(K-1)
# sig = np.ones(K-1)
print("mu: ", mu)
print("sig: ", sig)
Sigma = np.diag(sig)
# Add some covariance
# Sigma[:5,:5] = 1.0 + 1e-3*np.random.randn(5,5)
# Sample a bunch of pis and look at the marginals
pgm = PGMultinomial(K, mu=mu, Sigma=Sigma)
samples = 10000
pis = []
for smpl in xrange(samples):
pgm.resample()
pis.append(pgm.pi)
pis = np.array(pis)
print("E[pi]: ", pis.mean(axis=0))
print("var[pi]: ", pis.var(axis=0))
plt.figure()
plt.subplot(121)
plt.boxplot(pis)
plt.xlabel("k")
plt.ylabel("$p(\pi_k)$")
# Plot the covariance
cov = np.cov(pis.T)
plt.subplot(122)
plt.imshow(cov, interpolation="None", cmap="cool")
plt.colorbar()
plt.title("Cov($\pi$)")
plt.show()
def test_pgm_rvs():
K = 10
mu, sig = compute_uniform_mean_psi(K, sigma=2)
# mu = np.zeros(K-1)
# sig = np.ones(K-1)
print("mu: ", mu)
print("sig: ", sig)
Sigma = np.diag(sig)
# Add some covariance
# Sigma[:5,:5] = 1.0 + 1e-3*np.random.randn(5,5)
# Sample a bunch of pis and look at the marginals
pgm = PGMultinomial(K, mu=mu, Sigma=Sigma)
samples = 10000
pis = []
for smpl in range(samples):
pgm.resample()
pis.append(pgm.pi)
pis = np.array(pis)
print("E[pi]: ", pis.mean(axis=0))
print("var[pi]: ", pis.var(axis=0))
plt.figure()
plt.subplot(121)
plt.boxplot(pis)
plt.xlabel("k")
plt.ylabel("$p(\pi_k)$")
# Plot the covariance
cov = np.cov(pis.T)
plt.subplot(122)
plt.imshow(cov, interpolation="None", cmap="cool")
plt.colorbar()
plt.title("Cov($\pi$)")
plt.show()
def geweke_test(K, N_iter=10000):
"""
"""
# Create a multinomial distribution
mu = np.zeros(K - 1)
mu[-1] = 1
Sigma = np.eye(K - 1)
pgm = PGMultinomial(K, mu=mu, Sigma=Sigma)
# Run a Geweke test
xs = []
samples = []
for itr in xrange(N_iter):
if itr % 10 == 0:
print("Iteration ", itr)
# Resample the data
x = pgm.rvs(10)
# Resample the PG-Multinomial parameters
pgm.resample(x)
# Update our samples
xs.append(x.copy())
samples.append(pgm.copy_sample())
# Check that the PG-Multinomial samples are distributed like the prior
psi_samples = np.array([s.psi for s in samples])
psi_mean = psi_samples.mean(0)
psi_std = psi_samples.std(0)
print("Mean bias: ", psi_mean, " +- ", psi_std)
# Make Q-Q plots
ind = K - 2
fig = plt.figure()
ax = fig.add_subplot(121)
psi_dist = norm(mu[ind], np.sqrt(Sigma[ind, ind]))
probplot(psi_samples[:, ind], dist=psi_dist, plot=ax)
fig.add_subplot(122)
_, bins, _ = plt.hist(psi_samples[:, ind], 20, normed=True, alpha=0.2)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, psi_dist.pdf(bincenters), 'r--', linewidth=1)
plt.show()