MODEL_FILENAME = 'temp_weights_eight_schools.h5'
d = 3
DATA_SHAPE = (2500, 3)
q = GaussianWithReparametrization(d=3, shape=DATA_SHAPE)
q(tf.zeros(DATA_SHAPE))
q.load_weights(MODEL_FILENAME)
z, mu, log_var = q(tf.zeros(DATA_SHAPE))
thetas, mu, tau = z[:, 0], z[:, 1], z[:, 2]
# Prior
N = 5000
mu_prior = np.random.normal(loc=0, scale=5, size=N)
tau_prior = halfcauchy.rvs(loc=0, scale=5, size=N)
thetas_prior = np.random.normal(loc=mu_prior, scale=tau_prior, size=N)
mask_tau = (np.log(tau_prior) > -2) & (np.log(tau_prior) < 2.8)
plt.figure()
plt.scatter(np.log(tau_prior[mask_tau]),
thetas_prior[mask_tau],
color='gray',
alpha=0.6)
plt.scatter(tf.math.log(tau), thetas, color='crimson', alpha=0.6)
plt.xlabel(r'$log(\tau)$')
plt.ylabel(r'$\theta$')
plt.legend(['True Posterior', 'q'])
npdf = lambda x, m, s: np.exp(-(x - m)**2 / (2 * (s**2))) / np.sqrt(2 * np.pi *
(s**2))
# Display the probability density function (``pdf``): x = np.linspace(halfcauchy.ppf(0.01), halfcauchy.ppf(0.99), 100) ax.plot(x, halfcauchy.pdf(x), 'r-', lw=5, alpha=0.6, label='halfcauchy pdf') # Alternatively, the distribution object can be called (as a function) # to fix the shape, location and scale parameters. This returns a "frozen" # RV object holding the given parameters fixed. # Freeze the distribution and display the frozen ``pdf``: rv = halfcauchy() ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = halfcauchy.ppf([0.001, 0.5, 0.999]) np.allclose([0.001, 0.5, 0.999], halfcauchy.cdf(vals)) # True # Generate random numbers: r = halfcauchy.rvs(size=1000) # And compare the histogram: ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) ax.legend(loc='best', frameon=False) plt.show()
def main():
# generate data
np.random.seed(0)
n = 1
m = 10000
mu = norm.rvs(0, 1, m)
sigma = halfcauchy.rvs(0, 1, m)
y = norm.rvs(mu, sigma, (n, m))
# set up model
with pm.Model():
mu_ = pm.Normal("mu", 0, 1)
sigma_ = pm.HalfCauchy("sigma", 1)
yt_ = pm.Normal("yt", 0, 1, shape=n)
pm.Deterministic("y", mu_ + yt_ * sigma_)
# y_ = pm.Normal("y", mu_, sigma_, shape=n)
# sample and save samples
trace = pm.sample(m, chains=1)
mu_samples = trace["mu"][:]
sigma_samples = trace["sigma"][:]
yt_samples = trace["yt"].T[:]
y_samples = trace["y"].T[:]
# plot 2-D figures
sc = 5
fs = rcParams["figure.figsize"]
rcParams["figure.figsize"] = (fs[0], fs[0])
rcParams["lines.linewidth"] = 2
rcParams["font.size"] = 14
fig, axes = plt.subplots(2, 2, constrained_layout=True)
ax = axes[0, 0]
ax.scatter(
yt_samples[0], mu_samples, marker=".", alpha=0.05, rasterized=True, color="r"
)
ax.set_xlim(-sc, sc)
ax.set_ylim(-sc, sc)
ax.set_ylabel("$\mu$")
ax.set_xticklabels([])
ax = axes[0, 1]
ax.scatter(
y_samples[0], mu_samples, marker=".", alpha=0.05, rasterized=True, color="r"
)
ax.set_xlim(-sc, sc)
ax.set_ylim(-sc, sc)
ax.set_yticklabels([])
ax.set_xticklabels([])
ax = axes[1, 0]
ax.scatter(
yt_samples[0], sigma_samples, marker=".", alpha=0.05, rasterized=True, color="r"
)
ax.set_xlim(-sc, sc)
ax.set_ylim(0, sc / 2)
ax.set_xlabel(r"$\tilde{y}_0$")
ax.set_ylabel("$\sigma$")
ax = axes[1, 1]
ax.scatter(
y_samples[0], sigma_samples, marker=".", alpha=0.05, rasterized=True, color="r"
)
ax.set_xlim(-sc, sc)
ax.set_ylim(0, sc / 2)
ax.set_yticklabels([])
ax.set_xlabel("$y_0$")
# save
plt.savefig("../images/realistic-funnel-b.svg", bbox_inches=0, transparent=True)
import matplotlib.pyplot as plt import numpy as np from scipy.stats import halfcauchy N = 1000 mu = np.random.normal(loc=0, scale=5, size=N) tau = halfcauchy.rvs(loc=0, scale=5, size=N) theta = np.random.normal(loc=mu, scale=tau, size=N) mask_tau = (np.log(tau) > -2) & (np.log(tau) < 3) plt.scatter(np.log(tau[mask_tau]), theta[mask_tau], color='gray', alpha=0.6) plt.show()