def create_node_mi(name, parents, minum, milb, miub, mibins):
node_mi = Node(name, parents=parents, rvname='continuous')
minames = node_mi.discretize(milb, miub, minum, infinity='+-', bins=mibins)
node_insp = parents[0]
node_ai = parents[1]
ainum = node_ai.nstates()
labels = itertools.product(np.arange(node_insp.nstates()), np.arange(ainum))
labels = [label for label in labels]
for i,label in enumerate(labels):
if label[0] == 0: #no inspection
probs = 1./minum * np.ones(minum)
else: # with insepction
if label[0] == 1:
lmd = lmd1; beta = beta1
elif label[0] == 2:
lmd = lmd2; beta = beta2
elif label[0] == 3:
lmd = lmd3; beta = beta3
rvnames = ['Ai']
rvs = [node_ai.truncate_rv(label[1], lmd=trunclmd)]
aimean = rvs[0].stats('m')[()]
rv_am = stats.norm(aimean, sigmae)
pod = 1.-stats.norm.cdf((np.log(aimean)-lmd)/beta)
probs = rv_am.cdf(node_mi.bins[1:])-rv_am.cdf(node_mi.bins[:-1])
probs = probs/np.sum(probs)*pod
probs[0] = probs[0]+(1.-pod)
node_mi.assign_cpt(probs,label=np.asarray(label),statenames=node_mi.statenames)
# print 'labels: {}, progress: {}%, prob: {}'.format(label,
# float(i)/len(labels)*100, np.array_str(probs,precision=3))
return node_mi
def create_node_a(name,
parents,
ainum,
ailb,
aiub,
aiedges,
node_repair=None,
asmp0=None):
if node_repair is None:
node_ai = Node(name, parents=parents, rvname='continuous')
else:
node_ai = Node(name,
parents=parents + [node_repair],
rvname='continuous')
# dynamic discretization of nodes a and M
node_ap = parents[0]
knum = parents[1].nstates()
mnum = parents[2].nstates()
ainames = node_ai.discretize(ailb, aiub, ainum, infinity='+', bins=aiedges)
aibins = node_ai.bins
if node_repair is None:
labels = itertools.product(np.arange(node_ap.nstates()),
np.arange(knum), np.arange(mnum))
else:
labels = itertools.product(np.arange(node_ap.nstates()),
np.arange(knum), np.arange(mnum),
np.arange(2))
labels = [label for label in labels]
for i, label in enumerate(labels):
if len(label) == 4 and label[-1] == 1:
binnum, dummy = np.histogram(asmp0, aibins)
probs = binnum / np.sum(binnum, dtype=float)
node_ai.assign_cpt(probs,
label=np.asarray(label),
statenames=node_ai.statenames)
else:
truncrvs = []
for j, pstate in enumerate(label):
truncrvs.append(node_ai.parents[j].truncate_rv(pstate,
lmd=trunclmd))
rvnames = ['Ap', 'K', 'M']
rvs = truncrvs[:3]
probs, smpdb = mc2ai(rvnames, rvs, node_ai.bins, acrit, nsmp=nsmp)
# clean Ai states given Ai-1
apstate = label[0]
aplb = node_ap.bins[apstate]
aiubs = node_ai.bins[1:]
probs[aiubs <= aplb] = 0.
probs = probs / np.sum(probs)
node_ai.assign_cpt(probs,
label=np.asarray(label),
statenames=node_ai.statenames)
# print 'labels: {}, progress: {}%, prob: {}'.format(label,
# float(i)/len(labels)*100, np.array_str(probs,precision=3))
return node_ai
def create_node_mi(name, parents, minum, milb, miub, mibins):
node_mi = Node(name, parents=parents, rvname='continuous')
minames = node_mi.discretize(milb, miub, minum, infinity='+-', bins=mibins)
node_insp = parents[0]
node_ai = parents[1]
ainum = node_ai.nstates()
labels = itertools.product(np.arange(node_insp.nstates()),
np.arange(ainum))
labels = [label for label in labels]
for i, label in enumerate(labels):
if label[0] == 0: #no inspection
probs = 1. / minum * np.ones(minum)
else: # with insepction
if label[0] == 1:
lmd = lmd1
beta = beta1
elif label[0] == 2:
lmd = lmd2
beta = beta2
elif label[0] == 3:
lmd = lmd3
beta = beta3
rvnames = ['Ai']
rvs = [node_ai.truncate_rv(label[1], lmd=trunclmd)]
aimean = rvs[0].stats('m')[()]
rv_am = stats.norm(aimean, sigmae)
pod = 1. - stats.norm.cdf((np.log(aimean) - lmd) / beta)
probs = rv_am.cdf(node_mi.bins[1:]) - rv_am.cdf(node_mi.bins[:-1])
probs = probs / np.sum(probs) * pod
probs[0] = probs[0] + (1. - pod)
node_mi.assign_cpt(probs,
label=np.asarray(label),
statenames=node_mi.statenames)
# print 'labels: {}, progress: {}%, prob: {}'.format(label,
# float(i)/len(labels)*100, np.array_str(probs,precision=3))
return node_mi
def create_node_a(name, parents, ainum, ailb, aiub, aiedges, node_repair=None, asmp0=None):
if node_repair is None:
node_ai = Node(name, parents=parents, rvname='continuous')
else:
node_ai = Node(name, parents=parents+[node_repair], rvname='continuous')
# dynamic discretization of nodes a and M
node_ap = parents[0]
knum = parents[1].nstates()
mnum = parents[2].nstates()
ainames = node_ai.discretize(ailb, aiub, ainum, infinity='+', bins=aiedges)
aibins = node_ai.bins
if node_repair is None:
labels = itertools.product(np.arange(node_ap.nstates()), np.arange(knum),np.arange(mnum))
else:
labels = itertools.product(np.arange(node_ap.nstates()), np.arange(knum),
np.arange(mnum), np.arange(2))
labels = [label for label in labels]
for i,label in enumerate(labels):
if len(label)==4 and label[-1] == 1:
binnum,dummy = np.histogram(asmp0, aibins)
probs = binnum/np.sum(binnum, dtype=float)
node_ai.assign_cpt(probs,label=np.asarray(label),statenames=node_ai.statenames)
else:
truncrvs=[]
for j,pstate in enumerate(label):
truncrvs.append(node_ai.parents[j].truncate_rv(pstate,lmd=trunclmd))
rvnames = ['Ap', 'K', 'M']
rvs = truncrvs[:3]
probs,smpdb = mc2ai(rvnames, rvs, node_ai.bins, acrit, nsmp=nsmp)
# clean Ai states given Ai-1
apstate = label[0]
aplb = node_ap.bins[apstate]
aiubs = node_ai.bins[1:]
probs[aiubs<=aplb] = 0.
probs = probs/np.sum(probs)
node_ai.assign_cpt(probs,label=np.asarray(label),statenames=node_ai.statenames)
# print 'labels: {}, progress: {}%, prob: {}'.format(label,
# float(i)/len(labels)*100, np.array_str(probs,precision=3))
return node_ai
from pyNetica import Network, Node
import numpy as np
# create new net
netp = Network("ChestClinic")
# define nodes
visitAsia = Node("VisitAsia", parents=None, rvname='discrete')
smoking = Node("Smoking", parents=None, rvname='discrete')
tuberculosis = Node("Tuberculosis", parents=[visitAsia], rvname='discrete')
cancer = Node("Cancer", parents=[smoking], rvname='discrete')
tbOrCa = Node("TbOrCa", parents=[tuberculosis, cancer], rvname='discrete')
xRay = Node("XRay", parents=[tbOrCa], rvname='discrete')
# assign CPT
visitAsiaCpt = np.array([0.01, 0.99])[np.newaxis, :]
visitAsia.assign_cpt(visitAsiaCpt, statenames=['visit', 'no_visit'])
smokingCpt = np.array([0.50, 0.50])[np.newaxis, :]
smoking.assign_cpt(smokingCpt, statenames=['smoker', 'nonsmoker'])
tuberCpt = np.array([[0.05, 0.95], [0.01, 0.99]])
tuberculosis.assign_cpt(tuberCpt, statenames=['present', 'absent'])
cancerCpt = np.array([[0.10, 0.90], [0.01, 0.99]])
cancer.assign_cpt(cancerCpt, statenames=['present', 'absent'])
tbOrCaCpt = np.array([[1.0, 0.0], [1.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
tbOrCa.assign_cpt(tbOrCaCpt, statenames=['true', 'false'])
xRayCpt = np.array([[0.98, 0.02], [0.05, 0.95]])
xRay.assign_cpt(xRayCpt, statenames=['abnormal', 'normal'])
# add node
netp.add_nodes([visitAsia])
netp.add_nodes([smoking])
# beta = (50.*0.4)/(np.pi/np.sqrt(6))
# mu = 50.-np.euler_gamma*beta
# h = stats.gumbel_r(loc=mu, scale=beta)
urlogmean = np.log(35./np.sqrt(1+0.286**2))
urlogstd = np.sqrt(np.log(1+0.286**2))
uh = stats.lognorm(urlogstd, scale=np.exp(urlogmean))
theta = (60*0.2)**2/60.
k = 60./theta
v = stats.gamma(k, scale=theta)
# network model
# create nodes
r5 = Node("R5", parents=None, rvname='lognormal', rv=rv5)
r4 = Node("R4", parents=[r5], rvname='lognormal', rv=rv4)
m4 = Node("M4", parents=[r4], rvname='continuous')
m5 = Node("M5", parents=[r5], rvname='continuous')
q = Node("Q", parents=[r4,r5], rvname='continuous')
uh = Node("Uh", parents=None, rvname='lognormal', rv=uh)
e0 = Node("E0", parents=None, rvname='discrete')
earray = [e0]
life = 10; harray=[]
for i in range(life):
h = Node("H"+str(i+1), parents=[uh], rvname='continuous')
e = Node("E"+str(i+1),parents=[earray[-1],q,h], rvname='discrete')
harray.append(h)
earray.append(e)
# discretize continuous rv
from pyNetica import Network, Node
import numpy as np
# create new net
netp = Network("ChestClinic")
# define nodes
visitAsia = Node("VisitAsia", parents=None, rvname='discrete')
smoking = Node("Smoking", parents=None, rvname='discrete')
tuberculosis = Node("Tuberculosis", parents=[visitAsia], rvname='discrete')
cancer = Node("Cancer", parents=[smoking], rvname='discrete')
tbOrCa = Node("TbOrCa", parents=[tuberculosis, cancer], rvname='discrete')
xRay = Node("XRay", parents=[tbOrCa], rvname='discrete')
# assign CPT
visitAsiaCpt = np.array([0.01, 0.99])[np.newaxis, :]
visitAsia.assign_cpt(visitAsiaCpt, statenames=['visit','no_visit'])
smokingCpt = np.array([0.50, 0.50])[np.newaxis, :]
smoking.assign_cpt(smokingCpt, statenames=['smoker','nonsmoker'])
tuberCpt = np.array([[0.05, 0.95], [0.01, 0.99]])
tuberculosis.assign_cpt(tuberCpt, statenames=['present','absent'])
cancerCpt = np.array([[0.10, 0.90], [0.01, 0.99]])
cancer.assign_cpt(cancerCpt, statenames=['present','absent'])
tbOrCaCpt = np.array([[1.0, 0.0], [1.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
tbOrCa.assign_cpt(tbOrCaCpt, statenames=['true','false'])
xRayCpt = np.array([[0.98, 0.02], [0.05, 0.95]])
xRay.assign_cpt(xRayCpt, statenames=['abnormal','normal'])
# add node
netp.add_nodes([visitAsia])
netp.add_nodes([smoking])
theta = (60*0.2)**2/60.
k = 60./theta
v = stats.gamma(k, scale=theta)
rolnR = 0.3
# prior reliability using pyStRe
rvnames = ['ur', 'u1', 'u2', 'u3', 'u4', 'u5', 'h', 'v']
rvs = [ur, u1, u2, u3, u4, u5, h, v]
syspf = sys_prior(rvnames, rvs, rolnR)
print "Prior system failure probability is {}".format(syspf)
print "Prior system reliability is {}".format(stats.norm.ppf(1-syspf))
# network model
# create nodes
r5 = Node("R5", parents=None, rvname='lognormal', rv=rv5)
r4 = Node("R4", parents=[r5], rvname='lognormal', rv=rv4)
m4 = Node("M4", parents=[r4], rvname='continuous')
m5 = Node("M5", parents=[r5], rvname='continuous')
e = Node("E",parents=[r4,r5], rvname='discrete')
# discretize continuous rv
r4num = 20+1
r5num = 20+1
m4num = 20+2
m5num = 20+2
m = r5.rv.stats('m'); s = np.sqrt(r5.rv.stats('v'))
lb = 50.; ub = 250.
r4bins = np.hstack((0, np.linspace(lb, ub, r4num-1)))
r4names = r4.discretize(lb, ub, r4num, infinity='+', bins=r4bins)
m4names = m4.discretize(lb, ub, m4num, infinity='+-', bins=r4bins)
theta = (60 * 0.2)**2 / 60.
k = 60. / theta
v = stats.gamma(k, scale=theta)
rolnR = 0.3
# prior reliability using pyStRe
rvnames = ['ur', 'u1', 'u2', 'u3', 'u4', 'u5', 'h', 'v']
rvs = [ur, u1, u2, u3, u4, u5, h, v]
syspf = sys_prior(rvnames, rvs, rolnR)
print "Prior system failure probability is {}".format(syspf)
print "Prior system reliability is {}".format(stats.norm.ppf(1 - syspf))
# network model
# create nodes
r5 = Node("R5", parents=None, rvname='lognormal', rv=rv5)
r4 = Node("R4", parents=[r5], rvname='lognormal', rv=rv4)
m4 = Node("M4", parents=[r4], rvname='continuous')
m5 = Node("M5", parents=[r5], rvname='continuous')
e = Node("E", parents=[r4, r5], rvname='discrete')
# discretize continuous rv
r4num = 20 + 1
r5num = 20 + 1
m4num = 20 + 2
m5num = 20 + 2
m = r5.rv.stats('m')
s = np.sqrt(r5.rv.stats('v'))
lb = 50.
ub = 250.
r4bins = np.hstack((0, np.linspace(lb, ub, r4num - 1)))
from pyNetica import Node, Network
from pyNetica.netica import DECISION_NODE, UTILITY_NODE
from scipy import stats
import numpy as np
import itertools
import sys
from bnexample1_funcs import form2y
# random variables
rvX1 = stats.lognorm(1., scale=np.exp(0))
rvX3 = stats.lognorm(1., scale=np.exp(3*np.sqrt(2)))
# create nodes
weather = Node("Weather", parents=None, rvname='discrete')
forecast = Node("Forecast", parents=[weather], rvname='discrete')
umbrella = Node("Umbrella", parents=[forecast], rvname='discrete')
satisfy = Node("Satisfaction", parents=[weather, umbrella], rvname='deterministic')
umbrella.set_node_kind(DECISION_NODE)
satisfy.set_node_kind(UTILITY_NODE)
# assign CPT
# node weather
weathercpt = np.array([[0.7, 0.3]])
weather.assign_cpt(weathercpt, statenames=['sunshine', 'rain'])
# node forecast
forecastcpt = np.array([[0.7, 0.2, 0.1], [0.15, 0.25, 0.6]])
forecast.assign_cpt(forecastcpt, statenames=['sunny', 'cloudy', 'rainy'])
# node umbrella
umbrella.set_node_state_name(['take_umbrella', 'dont_take_umbrella'])
# node satisfy
loc=mmean, scale=mstd) # testing error, normal with mean=0, std=15kNm
# beta = (50.*0.4)/(np.pi/np.sqrt(6))
# mu = 50.-np.euler_gamma*beta
# h = stats.gumbel_r(loc=mu, scale=beta)
urlogmean = np.log(35. / np.sqrt(1 + 0.286**2))
urlogstd = np.sqrt(np.log(1 + 0.286**2))
uh = stats.lognorm(urlogstd, scale=np.exp(urlogmean))
theta = (60 * 0.2)**2 / 60.
k = 60. / theta
v = stats.gamma(k, scale=theta)
# network model
# create nodes
r5 = Node("R5", parents=None, rvname='lognormal', rv=rv5)
r4 = Node("R4", parents=[r5], rvname='lognormal', rv=rv4)
m4 = Node("M4", parents=[r4], rvname='continuous')
m5 = Node("M5", parents=[r5], rvname='continuous')
q = Node("Q", parents=[r4, r5], rvname='continuous')
uh = Node("Uh", parents=None, rvname='lognormal', rv=uh)
e0 = Node("E0", parents=None, rvname='discrete')
earray = [e0]
life = 10
harray = []
for i in range(life):
h = Node("H" + str(i + 1), parents=[uh], rvname='continuous')
e = Node("E" + str(i + 1),
parents=[earray[-1], q, h],
rvname='discrete')
harray.append(h)
if __name__ == '__main__':
# random variables
rv_a0 = stats.norm(0.5, 0.5*0.1)
rv_m = stats.norm(3.0, 3.0*0.05)
[logmean, logstd] = lognstats(2.3e-12, 0.3*2.3e-12)
# [logmean, logstd] = lognstats(4.5e-13, 0.3*4.5e-13)
rv_C = stats.lognorm(logstd, scale=np.exp(logmean))
[wblscale, wblc] = wblstats(22.5, 0.1*22.5)
rv_Sre = stats.weibull_min(wblc, scale=wblscale)
[logmean, logstd] = lognstats(2e6, 0.1*2e6)
rv_Na = stats.lognorm(logstd, scale=np.exp(logmean))
# network model
# create time-independent nodes
node_m = Node("M", parents=None, rvname='normal', rv=rv_m)
node_k = Node("K", parents=[node_m], rvname='continuous')
node_a0 = Node('a0', parents=None, rvname='normal', rv=rv_a0)
# discretize continuous rv
# node a0
a0num = 20+2
mu,var = rv_a0.stats(); sigma = np.sqrt(var)
lb = mu-3.*sigma; ub = mu+3.*sigma
a0bins = np.linspace(lb, ub, a0num-1)
a0names = node_a0.discretize(lb, ub, a0num, infinity='+-', bins=a0bins)
# node m
mnum = 20+2
mu,var = rv_m.stats(); sigma = np.sqrt(var)
lb = mu-3.*sigma; ub = mu+3.*sigma
mbins = np.linspace(lb, ub, mnum-1)
mnames = node_m.discretize(lb, ub, mnum, infinity='+-', bins=mbins)
from pyNetica import Node, Network
from scipy import stats
import numpy as np
import itertools
import sys
from bnexample1_funcs import form2y
# random variables
rvX1 = stats.lognorm(1., scale=np.exp(0))
rvX3 = stats.lognorm(1., scale=np.exp(3*np.sqrt(2)))
# create nodes
x1 = Node("X1", parents=None, rvname='lognormal', rv=rvX1)
x2 = Node("X2", parents=[x1], rvname='continuous')
y = Node("Y", parents=[x2], rvname='discrete')
# discretize continuous rv
x1num = 5
x2num = 5
m = x1.rv.stats('m'); s = np.sqrt(x1.rv.stats('v'))
#lb = np.maximum(0, m-2*s); ub = m+2*s
lb = 0.; ub = m+1.5*s
x1names = x1.discretize(lb, ub, x1num, infinity='+')
x2names = x2.discretize(lb*10., ub*10., x2num, infinity='+')
# calculate and assign CPT
# node X1
x1cpt = x1.rv.cdf(x1.bins[1:]) - x1.rv.cdf(x1.bins[:-1])
x1cpt = x1cpt[np.newaxis,:]
x1.assign_cpt(x1cpt, statenames=x1names)
acrit = 30.
life=5; lifearray = np.arange(life)+1.
# random variables
rv_a0 = stats.norm(0.5, 0.5*0.1)
rv_m = stats.norm(3.0, 3.0*0.05)
[logmean, logstd] = lognstats(2.3e-12, 0.3*2.3e-12)
# [logmean, logstd] = lognstats(4.5e-13, 0.3*4.5e-13)
rv_C = stats.lognorm(logstd, scale=np.exp(logmean))
[wblscale, wblc] = wblstats(22.5, 0.1*22.5)
rv_Sre = stats.weibull_min(wblc, scale=wblscale)
[logmean, logstd] = lognstats(2e6, 0.1*2e6)
rv_Na = stats.lognorm(logstd, scale=np.exp(logmean))
# network model
# create nodes
node_m = Node("M", parents=None, rvname='normal', rv=rv_m)
node_k = Node("K", parents=[node_m], rvname='continuous')
node_a0 = Node('a0', parents=None, rvname='normal', rv=rv_a0)
aarray = [node_a0]
marray=[]
for i in range(life):
ai = Node("A"+str(i+1), parents=[aarray[-1], node_k, node_m], rvname='continuous')
mi = Node("M"+str(i+1), parents=[ai], rvname='continuous')
aarray.append(ai)
marray.append(mi)
# discretize continuous rv
# node a0
a0num = 20+2
mu,var = rv_a0.stats(); sigma = np.sqrt(var)
lb = mu-3.*sigma; ub = mu+3.*sigma
if __name__ == '__main__':
# random variables
rv_a0 = stats.norm(0.5, 0.5 * 0.1)
rv_m = stats.norm(3.0, 3.0 * 0.05)
[logmean, logstd] = lognstats(2.3e-12, 0.3 * 2.3e-12)
# [logmean, logstd] = lognstats(4.5e-13, 0.3*4.5e-13)
rv_C = stats.lognorm(logstd, scale=np.exp(logmean))
[wblscale, wblc] = wblstats(22.5, 0.1 * 22.5)
rv_Sre = stats.weibull_min(wblc, scale=wblscale)
[logmean, logstd] = lognstats(2e6, 0.1 * 2e6)
rv_Na = stats.lognorm(logstd, scale=np.exp(logmean))
# network model
# create time-independent nodes
node_m = Node("M", parents=None, rvname='normal', rv=rv_m)
node_k = Node("K", parents=[node_m], rvname='continuous')
node_a0 = Node('a0', parents=None, rvname='normal', rv=rv_a0)
# discretize continuous rv
# node a0
a0num = 20 + 2
mu, var = rv_a0.stats()
sigma = np.sqrt(var)
lb = mu - 3. * sigma
ub = mu + 3. * sigma
a0bins = np.linspace(lb, ub, a0num - 1)
a0names = node_a0.discretize(lb, ub, a0num, infinity='+-', bins=a0bins)
# node m
mnum = 20 + 2
mu, var = rv_m.stats()
sigma = np.sqrt(var)
if __name__ == '__main__':
# random variables
rv_a0 = stats.norm(0.5, 0.5 * 0.1)
rv_m = stats.norm(3.0, 3.0 * 0.05)
[logmean, logstd] = lognstats(2.3e-12, 0.3 * 2.3e-12)
# [logmean, logstd] = lognstats(4.5e-13, 0.3*4.5e-13)
rv_C = stats.lognorm(logstd, scale=np.exp(logmean))
[wblscale, wblc] = wblstats(22.5, 0.1 * 22.5)
rv_Sre = stats.weibull_min(wblc, scale=wblscale)
[logmean, logstd] = lognstats(2e6, 0.1 * 2e6)
rv_Na = stats.lognorm(logstd, scale=np.exp(logmean))
# network model
# create nodes
node_m = Node("M", parents=None, rvname='normal', rv=rv_m)
node_k = Node("K", parents=[node_m], rvname='continuous')
node_a0 = Node('a0', parents=None, rvname='normal', rv=rv_a0)
aarray = [node_a0]
marray = []
for i in range(life):
ai = Node("A" + str(i + 1),
parents=[aarray[-1], node_k, node_m],
rvname='continuous')
mi = Node("M" + str(i + 1), parents=[ai], rvname='continuous')
aarray.append(ai)
marray.append(mi)
# discretize continuous rv
# node a0
a0num = 20 + 2
from pyNetica import Node, Network
from pyNetica.netica import DECISION_NODE, UTILITY_NODE
from scipy import stats
import numpy as np
import itertools
import sys
from bnexample1_funcs import form2y
# random variables
rvX1 = stats.lognorm(1., scale=np.exp(0))
rvX3 = stats.lognorm(1., scale=np.exp(3 * np.sqrt(2)))
# create nodes
weather = Node("Weather", parents=None, rvname='discrete')
forecast = Node("Forecast", parents=[weather], rvname='discrete')
umbrella = Node("Umbrella", parents=[forecast], rvname='discrete')
satisfy = Node("Satisfaction",
parents=[weather, umbrella],
rvname='deterministic')
umbrella.set_node_kind(DECISION_NODE)
satisfy.set_node_kind(UTILITY_NODE)
# assign CPT
# node weather
weathercpt = np.array([[0.7, 0.3]])
weather.assign_cpt(weathercpt, statenames=['sunshine', 'rain'])
# node forecast
forecastcpt = np.array([[0.7, 0.2, 0.1], [0.15, 0.25, 0.6]])
forecast.assign_cpt(forecastcpt, statenames=['sunny', 'cloudy', 'rainy'])
# node umbrella