def mv_simple():
mu = np.array([-.1, .5, 1.1])
p = np.array([
[2., 0, 0],
[.05, .1, 0],
[1., -0.05, 5.5]])
tau = np.dot(p, p.T)
with pm.Model() as model:
x = pm.MvNormal('x', pm.constant(mu), pm.constant(
tau), shape=3, testval=np.array([.1, 1., .8]))
H = tau
C = np.linalg.inv(H)
return model.test_point, model, (mu, C)
def mv_simple():
mu = np.array([-.1, .5, 1.1])
p = np.array([[2., 0, 0], [.05, .1, 0], [1., -0.05, 5.5]])
tau = np.dot(p, p.T)
with pm.Model() as model:
x = pm.MvNormal('x',
pm.constant(mu),
pm.constant(tau),
shape=3,
testval=np.array([.1, 1., .8]))
H = tau
C = np.linalg.inv(H)
return model.test_point, model, (mu, C)
def mv_simple_discrete():
d= 2
n = 5
p = np.array([.15,.85])
with pm.Model() as model:
x = pm.Multinomial('x', n, pm.constant(p), shape=d, testval=np.array([1,4]))
mu = n * p
#covariance matrix
C = np.zeros((d,d))
for (i, j) in product(range(d), range(d)):
if i == j:
C[i,i] = n * p[i]*(1-p[i])
else:
C[i,j] = -n*p[i]*p[j]
return model.test_point, model, (mu, C)
def mv_simple_discrete():
d = 2
n = 5
p = np.array([.15, .85])
with pm.Model() as model:
x = pm.Multinomial('x',
n,
pm.constant(p),
shape=d,
testval=np.array([1, 4]))
mu = n * p
#covariance matrix
C = np.zeros((d, d))
for (i, j) in product(range(d), range(d)):
if i == j:
C[i, i] = n * p[i] * (1 - p[i])
else:
C[i, j] = -n * p[i] * p[j]
return model.test_point, model, (mu, C)
import numpy as np
import matplotlib.pyplot as plt
import pymc as pm
k = 3
ndata = 500
spread = 5
centres = np.array([-spread, 0, spread])
v = np.random.randint(0, k, ndata)
data = centres[v] + np.random.randn(ndata)
l_res = plt.hist(data)
plt.show()
a = pm.constant(np.array([1., 1., 1.]))
p = pm.Dirichlet('p', a=a, shape=k)
p_min_potential = pm.Potential('p_min_potential',
tt.switch(tt.min(p) < .1, -np.inf, 0))
means = pm.Normal('means', mu=[0, 0, 0], sd=15, shape=k)
order_means_potential = pm.Potential(
'order_means_potential',
ttswitch(means[1] - means[0] < 0, -np.inf, 0) +
ttswitch(means[2] - means[1] < 0, -np.inf, 0))
