def sample_plot_gibbs(x0, z0, kv, π, μ, σ, n_iterations, xmin, xmax):
x_hist, z_hist = gibbs_sample(x0, z0, kv, π, μ, σ, n_iterations)
colors = ["tab:blue" if z else "tab:red" for z in z_hist]
fig, axs = plt.subplots()
axs.scatter(np.arange(n_iterations),
x_hist,
s=20,
facecolors="none",
edgecolors=colors)
pml.savefig("gibbs_scatter.pdf")
fig = plt.figure()
axs = plt.axes(projection="3d")
plot_gmm_3d_trace(x_hist, π, μ, σ, "Gibbs sampling", xmin, xmax, axs)
pml.style3d(axs, 1.5, 1, 0.8)
plt.subplots_adjust(left=0.001, bottom=0.208, right=0.7)
pml.savefig("gibbs_trace.pdf", pad_inches=0, bbox_inches="tight")
fig, axs = plt.subplots()
sm.graphics.tsa.plot_acf(x_hist,
lags=45,
alpha=None,
title="Gibbs",
ax=axs)
pml.savefig("gibbs_autocorrelation.pdf")
def sample_plot_mh(x0, τ, π, μ, σ, n_iterations, xmin, xmax):
x_hist = metropolis_sample(x0, τ, π, μ, σ, n_iterations)
fig = plt.figure()
axs = plt.axes(projection="3d")
plot_gmm_3d_trace(x_hist, π, μ, σ, f"MH with $N(0,{τ}^2)$ proposal", xmin,
xmax, axs)
pml.style3d(axs, 1.5, 1, 0.8)
plt.subplots_adjust(left=0.001, bottom=0.208)
pml.savefig(f"mh_trace_{τ}tau.pdf", pad_inches=0, bbox_inches="tight")
fig, axs = plt.subplots()
sm.graphics.tsa.plot_acf(x_hist,
lags=45,
alpha=None,
title=f"MH with $N(0,{τ}^2)$ proposal",
ax=axs)
pml.savefig(f"mh_autocorrelation_{τ}tau.pdf")
def plot_3d_belief_state(mu_hist,
dim,
ax,
skip=3,
npoints=2000,
azimuth=-30,
elevation=30):
nsteps = len(mu_hist)
xmin, xmax = mu_hist[..., dim].min(), mu_hist[..., dim].max()
xrange = jnp.linspace(xmin, xmax, npoints).reshape(-1, 1)
res = np.apply_along_axis(lambda X: pml.kdeg(xrange, X[..., None], 0.5), 1,
mu_hist)
densities = res[..., dim]
for t in range(0, nsteps, skip):
tloc = t * np.ones(npoints)
px = densities[t]
ax.plot(tloc, xrange, px, c="tab:blue", linewidth=1)
ax.set_zlim(0, 1)
pml.style3d(ax, 1.8, 1.2, 0.7, 0.8)
ax.view_init(elevation, azimuth)
ax.set_xlabel(r"$t$", fontsize=13)
ax.set_ylabel(r"$x_{" f"d={dim}" ",t}$", fontsize=13)
ax.set_zlabel(r"$p(x_{d, t} \vert y_{1:t})$", fontsize=13)