def marginal_plot(self, Ms):
axs = self.get_ax()
self.plot_data(axs)
for x, ax in zip(self.X, axs):
xnew = np.array([[t, x[1], x[2]] for t in self.tau])
for M, c in zip(Ms, self.cols):
mu, s2 = taylor_first_order(M, xnew)
self.plot_prediction(ax, c, mu, s2)
plt.show()
def design_plot(self, Ms, DCs, designs):
axs = self.get_ax(len(DCs), height=3)
for x, dc, ax in zip(designs, DCs, axs):
ax.set_title(dc)
ax.plot([x[0], x[0]], [0, 1], c='k', linestyle='--')
xnew = np.array([[t, x[1], x[2]] for t in self.tau])
for M, c in zip(Ms, self.cols):
mu, s2 = taylor_first_order(M, xnew)
self.plot_prediction(ax, c, mu, s2)
plt.show()
def marginal_plot(self, Ms):
axs = self.get_ax()
self.plot_data(axs)
for x, ax in zip(self.X, axs):
xnew = np.array([[t, x[1], x[2]] for t in self.tau])
for M, c in zip(Ms, self.cols):
mu, s2 = taylor_first_order(M, xnew)
self.plot_prediction(ax, c, mu, s2)
axs[1].legend(self.legend, loc=3, fontsize=14)
plt.suptitle('Marginal predictive distributions')
plt.tight_layout(True)
plt.subplots_adjust(top=0.85)
plt.show()
def design_plot(self, Ms, DCs, designs):
axs = self.get_ax(len(DCs), height=3)
for x, dc, ax in zip(designs, DCs, axs):
ax.set_title(dc)
ax.plot([x[0], x[0]], [0, 1], c='k', linestyle='--')
xnew = np.array([[t, x[1], x[2]] for t in self.tau])
for M, c in zip(Ms, self.cols):
mu, s2 = taylor_first_order(M, xnew)
self.plot_prediction(ax, c, mu, s2)
plt.suptitle(
'Marginal predictive distributions at suggested next designs')
plt.tight_layout(True)
plt.subplots_adjust(top=0.85)
plt.show()
def test_taylor_first_order (self): M = SimpleModel() mu, s2 = taylor_first_order(M, Xs) assert mu.shape == (N,E) assert s2.shape == (N,E,E)
for M in Ms:
M.Sigma = laplace_approximation(M, X)
# Compute the marginal predictive distributions of each model.
graphics.marginal_plot(Ms)
"""
Model posteriors
"""
print("== Model posteriors ==")
mu = np.zeros((len(X), len(Ms), E)) # Means
s2 = np.zeros((len(X), len(Ms), E, E)) # Covariances
D = np.array([M.dim_p
for M in Ms]) # No. of model parameters for each model
for i, M in enumerate(Ms):
# First-order Taylor approximation of marginal predictive distribution
mu[:, i], s2[:, i] = taylor_first_order(M, X)
# Compute normalised Akaike weights
pis = akaike(Y, mu, s2, D)
print(" - Normalised Akaike weights")
for M, p in zip(Ms, pis):
print("%s: %.5f" % (M.name, p))
# Check for winner
if np.any(pis >= 0.999):
print("Model %s is the winner!" % Ms[np.argmax(pis)].name)
break
"""
Design the next experiment
"""
Xtest = generate_x_mesh() # Test points