def test_hamiltonian_chain_burn_in():
posterior = ToroidalGaussian()
chain = HamiltonianChain(posterior=posterior, start=[1, 0.1, 0.1])
steps = 10
chain.advance(steps)
burn = chain.estimate_burn_in()
assert 0 < burn <= steps
chain.autoselect_burn()
assert chain.burn == burn
def test_hamiltonian_chain_restore(tmp_path):
posterior = ToroidalGaussian()
chain = HamiltonianChain(posterior=posterior,
grad=posterior.gradient,
start=[1, 0.1, 0.1])
steps = 10
chain.advance(steps)
filename = tmp_path / "restore_file.npz"
chain.save(filename)
new_chain = HamiltonianChain.load(filename)
assert new_chain.n == chain.n
assert new_chain.probs == chain.probs
assert all(new_chain.get_last() == chain.get_last())
def test_hamiltonian_chain_advance_no_gradient():
posterior = ToroidalGaussian()
chain = HamiltonianChain(posterior=posterior, start=[1, 0.1, 0.1])
first_n = chain.n
steps = 10
chain.advance(steps)
assert chain.n == first_n + steps
chain.burn = 0
assert len(chain.get_parameter(0)) == chain.n
assert len(chain.get_parameter(1)) == chain.n
assert len(chain.get_parameter(2)) == chain.n
assert len(chain.probs) == chain.n
def test_hamiltonian_chain_take_step():
posterior = ToroidalGaussian()
chain = HamiltonianChain(posterior=posterior,
grad=posterior.gradient,
start=[1, 0.1, 0.1])
first_n = chain.n
chain.take_step()
assert chain.n == first_n + 1
chain.burn = 0
assert len(chain.get_parameter(0)) == chain.n
assert len(chain.get_parameter(1)) == chain.n
assert len(chain.get_parameter(2)) == chain.n
assert len(chain.probs) == chain.n
def test_hamiltonian_chain_advance_bounds(line_posterior):
chain = HamiltonianChain(
posterior=line_posterior,
start=[0.5, 0.1],
bounds=(array([0.45, 0.0]), array([0.55, 10.0])),
)
chain.advance(10)
gradient = array(chain.get_parameter(0))
assert all(gradient >= 0.45)
assert all(gradient <= 0.55)
offset = array(chain.get_parameter(1))
assert all(offset >= 0)
return -0.5 * r**2 / self.w2
def gradient(self, theta):
x, y, z = theta
R = sqrt(x**2 + y**2)
K = 1 - self.R0 / R
g = array([K * x, K * y, z])
return -g / self.w2
# create an instance of our posterior class
posterior = ToroidalGaussian()
# create the chain object
chain = HamiltonianChain(posterior=posterior,
grad=posterior.gradient,
start=[1, 0.1, 0.1])
# advance the chain to generate the sample
chain.advance(6000)
# choose how many samples will be thrown away from the start
# of the chain as 'burn-in'
chain.burn = 2000
chain.matrix_plot(filename='hmc_matrix_plot.png')
# extract sample and probability data from the chain
probs = chain.get_probabilities()
colors = exp(probs - max(probs))
xs, ys, zs = [chain.get_parameter(i) for i in [0, 1, 2]]
return -0.5 * r**2 / self.w2
def gradient(self, theta):
x, y, z = theta
R = sqrt(x**2 + y**2)
K = 1 - self.R0 / R
g = array([K * x, K * y, z])
return -g / self.w2
# create an instance of our posterior class
posterior = ToroidalGaussian()
# create the chain object
chain = HamiltonianChain(posterior=posterior,
grad=posterior.gradient,
start=[1, 0.1, 0.1])
# advance the chain to generate the sample
chain.advance(6000)
# choose how many samples will be thrown away from the start
# of the chain as 'burn-in'
chain.burn = 2000
# extract sample and probability data from the chain
probs = chain.get_probabilities()
colors = exp(probs - max(probs))
xs, ys, zs = [chain.get_parameter(i) for i in [0, 1, 2]]
# Plot the sample we've generated as a 3D scatterplot
return -0.5 * r**2 / self.w2
def gradient(self, theta):
x, y, z = theta
R = sqrt(x**2 + y**2)
K = 1 - self.R0 / R
g = array([K * x, K * y, z])
return -g / self.w2
posterior = ToroidalGaussian()
from inference.mcmc import HamiltonianChain
hmc = HamiltonianChain(posterior=posterior,
grad=posterior.gradient,
start=[1, 0.1, 0.1])
hmc.advance(6000)
hmc.burn = 1000
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure(figsize=(5, 4))
ax = fig.add_subplot(111, projection='3d')
ax.set_xticks([-1, -0.5, 0., 0.5, 1.])
ax.set_yticks([-1, -0.5, 0., 0.5, 1.])
ax.set_zticks([-1, -0.5, 0., 0.5, 1.])
# ax.set_title('Hamiltonian Monte-Carlo')
L = 1.1
ax.set_xlim([-L, L])
ax.set_ylim([-L, L])