def test_region_est_ellipsoid(self):
"""
Tests that region_est_ellipsoid works.
"""
dist = MultivariateNormalDistribution(self.MEAN, self.COV)
u = ParticleDistribution(
particle_locations = dist.sample(self.N_PARTICLES),
particle_weights = np.ones(self.N_PARTICLES)/self.N_PARTICLES
)
# ask for a confidence level of 0.5
A, c = u.region_est_ellipsoid(level=0.5)
# center of ellipse should be the mean of the multinormal
assert_almost_equal(np.round(c), self.MEAN, 1)
# finally, the principal lengths of the ellipsoid
# should be the same as COV
_, QA, _ = np.linalg.svd(A)
_, QC, _ = np.linalg.svd(self.COV)
QA, QC = np.sqrt(QA), np.sqrt(QC)
assert_almost_equal(
QA / np.linalg.norm(QA),
QC / np.linalg.norm(QC),
1
)
def test_est_credible_region(self):
"""
Tests that est_credible_region doesn't fail miserably
"""
dist = MultivariateNormalDistribution(self.MEAN, self.COV)
u = ParticleDistribution(
particle_locations = dist.sample(self.N_PARTICLES),
particle_weights = np.ones(self.N_PARTICLES)/self.N_PARTICLES
)
# first check that 0.95 confidence points consume 0.9 confidence points
points1 = u.est_credible_region(level=0.95)
points2 = u.est_credible_region(level=0.9)
assert_almost_equal(
np.sort(unique_rows(np.concatenate([points1, points2])), axis=0),
np.sort(points1, axis=0)
)
# do the same thing with different slice
points1 = u.est_credible_region(level=0.95, modelparam_slice=self.SLICE)
points2 = u.est_credible_region(level=0.9, modelparam_slice=self.SLICE)
assert_almost_equal(
np.sort(unique_rows(np.concatenate([points1, points2])), axis=0),
np.sort(points1, axis=0)
)
def test_region_est_hull(self):
"""
Tests that test_region_est_hull works
"""
dist = MultivariateNormalDistribution(self.MEAN, self.COV)
u = ParticleDistribution(
particle_locations = dist.sample(self.N_PARTICLES),
particle_weights = np.ones(self.N_PARTICLES)/self.N_PARTICLES
)
faces, vertices = u.region_est_hull(level=0.95)
# In this multinormal case, the convex hull surface
# should be centered at MEAN
assert_almost_equal(
np.round(np.mean(vertices, axis=0)),
np.round(self.MEAN)
)
# And a lower level should result in a smaller hull
# and therefore smaller sample variance
faces2, vertices2 = u.region_est_hull(level=0.2)
assert_array_less(np.var(vertices2, axis=0), np.var(vertices, axis=0))
def test_in_credible_region(self):
"""
Tests that in_credible_region works.
"""
dist = MultivariateNormalDistribution(self.MEAN, self.COV)
u = ParticleDistribution(
particle_locations = dist.sample(self.N_PARTICLES),
particle_weights = np.ones(self.N_PARTICLES)/self.N_PARTICLES
)
# some points to test with
test_points = np.random.multivariate_normal(self.MEAN, self.COV, self.N_PARTICLES)
# method='pce'
results = [
u.in_credible_region(test_points, level=0.9, method='pce'),
u.in_credible_region(test_points, level=0.84, method='pce'),
u.in_credible_region(test_points, level=0.5, method='pce'),
]
assert_almost_equal(
np.array([np.mean(x.astype('float')) for x in results]),
np.array([0.9, 0.84, 0.5]),
3
)
# method='hpd-hull'
results1 = [
u.in_credible_region(test_points, level=0.9, method='hpd-hull'),
u.in_credible_region(test_points, level=0.84, method='hpd-hull'),
u.in_credible_region(test_points, level=0.5, method='hpd-hull'),
]
assert_array_less(
np.array([0.9, 0.84, 0.5]),
np.array([np.mean(x.astype('float')) for x in results1])
)
# method='hpd-mvee'
results2 = [
u.in_credible_region(test_points, level=0.9, method='hpd-mvee'),
u.in_credible_region(test_points, level=0.84, method='hpd-mvee'),
u.in_credible_region(test_points, level=0.5, method='hpd-mvee'),
]
assert_array_less(
np.array([0.9, 0.84, 0.5]),
np.array([np.mean(x.astype('float')) for x in results2])
)
# the mvee should be bigger than the convex hull.
# this passes iff all points in the ellipses are
# also in the hulls.
assert_array_less(
np.hstack([x.astype('float') for x in results1]),
np.hstack([x.astype('float') for x in results2]) + 0.5
)
# check for no failures with slices.
u.in_credible_region(test_points[:100,self.SLICE], level=0.9, method='pce', modelparam_slice=self.SLICE)
u.in_credible_region(test_points[:100,self.SLICE], level=0.9, method='hpd-hull', modelparam_slice=self.SLICE)
u.in_credible_region(test_points[:100,self.SLICE], level=0.9, method='hpd-mvee', modelparam_slice=self.SLICE)
# check for no failures with single inputs
assert(u.in_credible_region(test_points[0,:], level=0.9, method='pce').size == 1)
assert(u.in_credible_region(test_points[0,:], level=0.9, method='hpd-hull').size == 1)
assert(u.in_credible_region(test_points[0,:], level=0.9, method='hpd-mvee').size == 1)
