def test_gibbs_chain_non_negative(line_posterior):
chain = GibbsChain(posterior=line_posterior, start=[0.5, 0.1])
chain.set_non_negative(1)
chain.advance(100)
offset = array(chain.get_parameter(1))
assert all(offset >= 0)
def test_gibbs_chain_set_boundary(line_posterior):
chain = GibbsChain(posterior=line_posterior, start=[0.5, 0.1])
left, right = (0.45, 0.55)
chain.set_boundaries(0, [left, right])
chain.advance(100)
gradient = array(chain.get_parameter(0))
assert all(gradient >= left)
assert all(gradient <= right)
def test_gibbs_chain_remove_boundary(line_posterior):
chain = GibbsChain(posterior=line_posterior, start=[0.5, 0.1])
left, right = (0.45, 0.4500000000001)
chain.set_boundaries(0, [left, right])
chain.set_boundaries(0, None, remove=True)
chain.advance(100)
gradient = array(chain.get_parameter(0))
# Some values should be outside the original boundary
assert not all(gradient >= left) or not all(gradient <= right)
def test_gibbs_chain_get_parameter():
start_location = array([2.0, -4.0])
width_guesses = array([5.0, 0.05])
chain = GibbsChain(posterior=rosenbrock,
start=start_location,
widths=width_guesses)
steps = 5
chain.advance(steps)
samples = chain.get_parameter(0)
assert len(samples) == expected_len(steps)
burn = 2
samples = chain.get_parameter(0, burn=burn)
assert len(samples) == expected_len(steps, burn)
thin = 2
samples = chain.get_parameter(1, thin=thin)
assert len(samples) == expected_len(steps, step=thin)
samples = chain.get_parameter(1, burn=burn, thin=thin)
assert len(samples) == expected_len(steps, start=burn, step=thin)
width_guesses = array([5., 0.05])
# create the chain object
chain = GibbsChain(posterior=rosenbrock,
start=start_location,
widths=width_guesses)
# advance the chain 150k steps
chain.advance(150000)
# the samples for the n'th parameter can be accessed through the
# get_parameter(n) method. We could use this to plot the path of
# the chain through the 2D parameter space:
p = chain.get_probabilities() # color the points by their probability value
plt.scatter(chain.get_parameter(0),
chain.get_parameter(1),
c=exp(p - max(p)),
marker='.')
plt.xlabel('parameter 1')
plt.ylabel('parameter 2')
plt.grid()
plt.show()
# We can see from this plot that in order to take a representative sample,
# some early portion of the chain must be removed. This is referred to as
# the 'burn-in' period. This period allows the chain to both find the high
# density areas, and adjust the proposal widths to their optimal values.
# The plot_diagnostics() method can help us decide what size of burn-in to use:
# poor, to demonstrate that gibbs sampling allows each proposal width
# to be adjusted individually toward an optimal value.
width_guesses = array([5.,0.05])
# create the chain object
chain = GibbsChain(posterior = rosenbrock, start = start_location, widths = width_guesses)
# advance the chain 150k steps
chain.advance(150000)
# the samples for the n'th parameter can be accessed through the
# get_parameter(n) method. We could use this to plot the path of
# the chain through the 2D parameter space:
p = chain.get_probabilities() # color the points by their probability value
plt.scatter(chain.get_parameter(0), chain.get_parameter(1), c = exp(p-max(p)), marker = '.')
plt.xlabel('parameter 1')
plt.ylabel('parameter 2')
plt.grid()
plt.show()
# We can see from this plot that in order to take a representative sample,
# some early portion of the chain must be removed. This is referred to as
# the 'burn-in' period. This period allows the chain to both find the high
# density areas, and adjust the proposal widths to their optimal values.
# The plot_diagnostics() method can help us decide what size of burn-in to use:
chain.plot_diagnostics()
def rosenbrock(t):
x, y = t
x2 = x**2
b = 15. # correlation strength parameter
v = 3. # variance of the gaussian term
return -x2 - b * (y - x2)**2 - 0.5 * (x2 + y**2) / v
# create the chain object
from inference.mcmc import GibbsChain
gibbs = GibbsChain(posterior=rosenbrock, start=array([2., -4.]))
gibbs.advance(150000)
gibbs.burn = 10000
gibbs.thin = 70
p = gibbs.get_probabilities() # color the points by their probability value
fig = plt.figure(figsize=(5, 4))
ax1 = fig.add_subplot(111)
ax1.scatter(gibbs.get_parameter(0),
gibbs.get_parameter(1),
c=exp(p - max(p)),
marker='.')
ax1.set_ylim([None, 2.8])
ax1.set_xlim([-1.8, 1.8])
ax1.set_xticks([])
ax1.set_yticks([])
# ax1.set_title('Gibbs sampling')
plt.tight_layout()
plt.savefig('gallery_gibbs_sampling.png')
plt.show()
