def test_convergence_with_map (self):
""" Tests if we can still achieve convergence when using
parallel_map. """
mu = [2, 1]
s = [[.01, 0], [0, .01]]
X = MultivariateLognormal (mu, s)
N = 2000
rvs_caller = lambda _: X.rvs ()
rand_vals = parallel_map (rvs_caller, range (N), 5)
mean = np.array ([.0, .0])
for val in rand_vals:
mean += val
mean /= N
assert all (abs (X.mean () - mean) / X.mean () < 1e-1)
mu = [2, 1]
s = [[.01, 0], [0, .01]]
X = MultivariateLognormal (mu, s)
N = 2000
rvs_caller = lambda _: X.rvs ()
rand_vals = parallel_map (rvs_caller, range (N), 5)
mean = np.array ([.0, .0])
for val in rand_vals:
mean += val
mean /= N
assert all (abs (X.mean () - mean) / X.mean () < 1e-1)
def __init__ (self, theta):
super ().__init__ (theta, verbose=False)
n = theta.get_size ()
mu = np.ones (n)
Sigma = np.eye (n) / 10
self.target_distribution = MultivariateLognormal (mu,
Sigma)
def test_get_random_value (self):
""" Tests if one can get the a random value from the random
variable. """
mu = [2, 1]
s = [[1, 0], [0, 1]]
X = MultivariateLognormal (mu, s)
X_0 = X.rvs ()
assert all (X_0 > 0)
def test_get_mean (self):
""" Tests if one can get the mean of the random variable. """
mu = [1, 2, 3, 4]
S = np.array ([[2, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 4, 1],
[0, 0, 1, 2]])
X = MultivariateLognormal (mu, S)
assert all (abs (X.mean () - np.exp (np.array (mu) \
+ S.diagonal () / 2)) < 1e-4)
def create_covar_matrix(self):
my_artificial_sample = []
sample_mean = [0.05, 0.1, 0.2, .3]
S = np.eye(4) / 5
mu = np.log(np.array(sample_mean)) - S.diagonal() / 2
my_sample_dist = MultivariateLognormal(mu, S)
for i in range(50):
values = my_sample_dist.rvs()
my_artificial_sample.append(values)
covar = calc_covariance(my_artificial_sample)
return covar
def test_get_pdf_of_small_prob_point (self):
""" Tests if we can get the pdf of a point with small pdf value.
"""
mu = [0, 0, 0]
S = [[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]
X = MultivariateLognormal (mu, S)
x = [1e-230, 1e-120, 1e-130]
analytic = 0
assert (abs (X.pdf (x) - analytic) < 1e-4)
def test_get_pdf_of_zero_prob_point (self):
""" Tests if we can get the pdf of a point with pdf equal to
zero. """
mu = [0, 0, 0]
S = [[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]
X = MultivariateLognormal (mu, S)
x = [1, 0, 1]
analytic = 0
assert (abs (X.pdf (x) - analytic) < 1e-4)
def test_get_pdf (self):
""" Tests if we can get a point of the probability density
function of this random variable. """
mu = [0, 0, 0]
S = [[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]
X = MultivariateLognormal (mu, S)
x = [1, 1, 1]
analytic = 1 / np.sqrt ((2 * np.pi) ** 3 )
assert (abs (X.pdf (x) - analytic) < 1e-4)
def _create_jump_dist (self, theta_t):
n = theta_t.get_size ()
s2 = np.eye (n) / 100
variances = s2.diagonal ()
theta_values = np.array (theta_t.get_values ())
mu = np.log (theta_values) - variances / 2
return MultivariateLognormal (mu, s2)
class MHMultivariateLognormalTargetMock (MetropolisHastings):
def __init__ (self, theta):
super ().__init__ (theta, verbose=False)
n = theta.get_size ()
mu = np.ones (n)
Sigma = np.eye (n) / 10
self.target_distribution = MultivariateLognormal (mu,
Sigma)
def _calc_log_likelihood (self, t):
t_values = t.get_values ()
l = self.target_distribution.pdf (t_values)
return np.log (l)
def _create_jump_dist (self, theta_t):
n = theta_t.get_size ()
S = np.eye (n) / 100
variances = S.diagonal ()
theta_values = np.array (theta_t.get_values ())
mu = np.log (theta_values) - variances / 2
return MultivariateLognormal (mu, S)
def _calc_mh_ratio (self, new_t, new_l, old_t, old_l):
J_gv_new = self._create_jump_dist (new_t)
J_gv_old = self._create_jump_dist (old_t)
p_old_gv_new = J_gv_new.pdf (old_t.get_values ())
p_new_gv_old = J_gv_old.pdf (new_t.get_values ())
l_ratio = np.exp (new_l - old_l)
r = (l_ratio) * (p_old_gv_new / p_new_gv_old)
return r
def create_starting_sample (self):
my_artificial_sample = []
log_likelihoods = []
sample_mean = [0.05, 0.1, 0.2, .3]
S = np.eye (4) / 5
mu = np.log (np.array (sample_mean)) - S.diagonal () / 2
my_sample_dist = MultivariateLognormal (mu, S)
for i in range (50):
theta = RandomParameterList ()
values = my_sample_dist.rvs ()
for v in values[:-1]:
p = RandomParameter ('p', Gamma (2, 2))
p.value = v
theta.append (p)
exp_error = RandomParameter ('sigma', Gamma (2, 2))
theta.set_experimental_error (exp_error)
log_likelihoods.append (1)
my_artificial_sample.append (theta)
return (my_artificial_sample, log_likelihoods)
def _create_jump_dist(self, theta_t):
""" The jump distribution is Multivariate Lognormal with a
diagonal covariance matrix, i.e the jumps on each parameter
are independent. """
n = theta_t.get_size()
t_vals = np.array(theta_t.get_values())
S = np.eye(n)
for i in range(n):
S[i, i] = self._jump_S[i]
mu = np.array(np.log(t_vals))
dist = MultivariateLognormal(mu, S)
return dist
def test_convergence_to_mean (self):
""" Tests if the randomly generated values has a sample mean
that converges to the correct mean. """
mu = [2, 1]
s = [[.01, 0], [0, .01]]
X = MultivariateLognormal (mu, s)
N = 2000
mean = np.array ([.0, .0])
for i in range (N):
mean += X.rvs ()
mean /= N
assert all (abs (X.mean () - mean) / X.mean () < 1e-1)
mu = [2, 1]
s = [[.01, 0], [0, .01]]
X = MultivariateLognormal (mu, s)
N = 2000
mean = np.array ([.0, .0])
for i in range (N):
mean += X.rvs ()
mean /= N
assert all (abs (X.mean () - mean) / X.mean () < 1e-1)
def test_create_shaped_distribution (self):
""" Tests if we can create a Multivariate Lognormal
distribution with a specified mean and variance. """
mu = [1, 2, .1]
S = np.array ([[.1, 0, 0],
[ 0, .2, 0],
[ 0, 0, .2]])
X = MultivariateLognormal.create_lognormal_with_shape (mu, S)
N = 2000
mean = np.array ([.0, .0, .0])
for i in range (N):
x = X.rvs ()
mean += x
mean /= N
assert all (abs (mu - mean) / mean < 2e-1)
def _create_jump_dist(self, theta_t):
""" Creates the jump distribution from the current point.
Parameters
theta_t: a RandomParameterList with the current point.
Returns
A MultivariateLognormal distribution which is the jump
distribution from the current point. This distribution
have the normal parametrization with
mu = log(current_point_values) and covariance equal
to the sample covariance of the log of the accepted
points.
"""
t_vals = theta_t.get_values()
mu = np.array(np.log(t_vals))
dist = MultivariateLognormal(mu, self._jump_S * self._jump_scale)
return dist
def _create_jump_dist (self, theta_t):
""" The jump distribution is Multivariate Lognormal. """
t_vals = theta_t.get_values ()
mu = np.log (t_vals) - jump_S.diagonal () / 2
jump_dist = MultivariateLognormal (mu, jump_S)
return jump_dist