def test_geweke():
"""
Create a discrete time Hawkes model and generate from it.
:return:
"""
K = 1
T = 50.0
dt = 1.0
dt_max = 3.0
# network_hypers = {'C': 1, 'p': 0.5, 'kappa': 3.0, 'alpha': 3.0, 'beta': 1.0/20.0}
network_hypers = {'c': np.zeros(K, dtype=np.int), 'p': 0.5, 'kappa': 10.0, 'v': 10*3.0}
bkgd_hypers = {"alpha": 1., "beta": 10.}
model = ContinuousTimeNetworkHawkesModel(K=K, dt_max=dt_max,
network_hypers=network_hypers)
model.generate(T=T)
# Gibbs sample and then generate new data
N_samples = 1000
samples = []
lps = []
for itr in progprint_xrange(N_samples, perline=50):
# Resample the model
model.resample_model()
samples.append(model.copy_sample())
lps.append(model.log_likelihood())
# Geweke step
model.data_list.pop()
model.generate(T=T)
# Compute sample statistics for second half of samples
A_samples = np.array([s.weight_model.A for s in samples])
W_samples = np.array([s.weight_model.W for s in samples])
mu_samples = np.array([s.impulse_model.mu for s in samples])
tau_samples = np.array([s.impulse_model.tau for s in samples])
lambda0_samples = np.array([s.bias_model.lambda0 for s in samples])
lps = np.array(lps)
offset = 0
A_mean = A_samples[offset:, ...].mean(axis=0)
W_mean = W_samples[offset:, ...].mean(axis=0)
mu_mean = mu_samples[offset:, ...].mean(axis=0)
tau_mean = tau_samples[offset:, ...].mean(axis=0)
lambda0_mean = lambda0_samples[offset:, ...].mean(axis=0)
print("A mean: ", A_mean)
print("W mean: ", W_mean)
print("mu mean: ", mu_mean)
print("tau mean: ", tau_mean)
print("lambda0 mean: ", lambda0_mean)
# Plot the log probability over iterations
plt.figure()
plt.plot(np.arange(N_samples), lps)
plt.xlabel("Iteration")
plt.ylabel("Log probability")
# Plot the histogram of bias samples
plt.figure()
p_lmbda0 = gamma(model.bias_model.alpha, scale=1./model.bias_model.beta)
_, bins, _ = plt.hist(lambda0_samples[:,0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5*(bins[1:]+bins[:-1])
plt.plot(bincenters, p_lmbda0.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('lam0')
plt.ylabel('p(lam0)')
print("Expected p(A): ", model.network.P)
print("Empirical p(A): ", A_samples.mean(axis=0))
# Plot the histogram of weight samples
plt.figure()
Aeq1 = A_samples[:,0,0] == 1
# p_W1 = gamma(model.network.kappa, scale=1./model.network.v[0,0])
# p_W1 = betaprime(model.network.kappa, model.network.alpha, scale=model.network.beta)
p_W1 = gamma(model.network.kappa, scale=1./model.network.v[0,0])
if np.sum(Aeq1) > 0:
_, bins, _ = plt.hist(W_samples[Aeq1,0,0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5*(bins[1:]+bins[:-1])
plt.plot(bincenters, p_W1.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('W')
plt.ylabel('p(W | A=1)')
# Plot the histogram of impulse precisions
plt.figure()
p_tau = gamma(model.impulse_model.alpha_0, scale=1./model.impulse_model.beta_0)
_, bins, _ = plt.hist(tau_samples[:,0,0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5*(bins[1:]+bins[:-1])
plt.plot(bincenters, p_tau.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('tau')
plt.ylabel('p(tau)')
# Plot the histogram of impulse means
plt.figure()
p_mu = t(df=2*model.impulse_model.alpha_0,
loc=model.impulse_model.mu_0,
scale=np.sqrt(model.impulse_model.beta_0/(model.impulse_model.alpha_0*model.impulse_model.lmbda_0)))
_, bins, _ = plt.hist(mu_samples[:,0,0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5*(bins[1:]+bins[:-1])
plt.plot(bincenters, p_mu.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('mu')
plt.ylabel('p(mu)')
plt.show()
def test_geweke():
"""
Create a discrete time Hawkes model and generate from it.
:return:
"""
K = 1
T = 50.0
dt = 1.0
dt_max = 3.0
# network_hypers = {'C': 1, 'p': 0.5, 'kappa': 3.0, 'alpha': 3.0, 'beta': 1.0/20.0}
network_hypers = {"c": np.zeros(K, dtype=np.int), "p": 0.5, "kappa": 10.0, "v": 10 * 3.0}
bkgd_hypers = {"alpha": 1.0, "beta": 10.0}
model = ContinuousTimeNetworkHawkesModel(K=K, dt_max=dt_max, network_hypers=network_hypers)
model.generate(T=T)
# Gibbs sample and then generate new data
N_samples = 1000
samples = []
lps = []
for itr in progprint_xrange(N_samples, perline=50):
# Resample the model
model.resample_model()
samples.append(model.copy_sample())
lps.append(model.log_likelihood())
# Geweke step
model.data_list.pop()
model.generate(T=T)
# Compute sample statistics for second half of samples
A_samples = np.array([s.weight_model.A for s in samples])
W_samples = np.array([s.weight_model.W for s in samples])
mu_samples = np.array([s.impulse_model.mu for s in samples])
tau_samples = np.array([s.impulse_model.tau for s in samples])
lambda0_samples = np.array([s.bias_model.lambda0 for s in samples])
lps = np.array(lps)
offset = 0
A_mean = A_samples[offset:, ...].mean(axis=0)
W_mean = W_samples[offset:, ...].mean(axis=0)
mu_mean = mu_samples[offset:, ...].mean(axis=0)
tau_mean = tau_samples[offset:, ...].mean(axis=0)
lambda0_mean = lambda0_samples[offset:, ...].mean(axis=0)
print "A mean: ", A_mean
print "W mean: ", W_mean
print "mu mean: ", mu_mean
print "tau mean: ", tau_mean
print "lambda0 mean: ", lambda0_mean
# Plot the log probability over iterations
plt.figure()
plt.plot(np.arange(N_samples), lps)
plt.xlabel("Iteration")
plt.ylabel("Log probability")
# Plot the histogram of bias samples
plt.figure()
p_lmbda0 = gamma(model.bias_model.alpha, scale=1.0 / model.bias_model.beta)
_, bins, _ = plt.hist(lambda0_samples[:, 0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_lmbda0.pdf(bincenters), "r--", linewidth=1)
plt.xlabel("lam0")
plt.ylabel("p(lam0)")
print "Expected p(A): ", model.network.P
print "Empirical p(A): ", A_samples.mean(axis=0)
# Plot the histogram of weight samples
plt.figure()
Aeq1 = A_samples[:, 0, 0] == 1
# p_W1 = gamma(model.network.kappa, scale=1./model.network.v[0,0])
# p_W1 = betaprime(model.network.kappa, model.network.alpha, scale=model.network.beta)
p_W1 = gamma(model.network.kappa, scale=1.0 / model.network.v[0, 0])
if np.sum(Aeq1) > 0:
_, bins, _ = plt.hist(W_samples[Aeq1, 0, 0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_W1.pdf(bincenters), "r--", linewidth=1)
plt.xlabel("W")
plt.ylabel("p(W | A=1)")
# Plot the histogram of impulse precisions
plt.figure()
p_tau = gamma(model.impulse_model.alpha_0, scale=1.0 / model.impulse_model.beta_0)
_, bins, _ = plt.hist(tau_samples[:, 0, 0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_tau.pdf(bincenters), "r--", linewidth=1)
plt.xlabel("tau")
plt.ylabel("p(tau)")
# Plot the histogram of impulse means
plt.figure()
p_mu = t(
df=2 * model.impulse_model.alpha_0,
loc=model.impulse_model.mu_0,
scale=np.sqrt(model.impulse_model.beta_0 / (model.impulse_model.alpha_0 * model.impulse_model.lmbda_0)),
)
_, bins, _ = plt.hist(mu_samples[:, 0, 0], bins=50, alpha=0.5, normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_mu.pdf(bincenters), "r--", linewidth=1)
plt.xlabel("mu")
plt.ylabel("p(mu)")
plt.show()
