import numpy as np
import pymc as pm
from matplotlib import pyplot as plt
N = 20
#create some artificial data.
lifetime = pm.rweibull(2, 5, size=N)
birth = pm.runiform(0, 10, N)
censor = (birth +
lifetime) > 10 #an individual is right-censored if this is True
lifetime_ = np.ma.masked_array(lifetime, censor) #create the censorship event.
lifetime_.set_fill_value(10) #good for computations later.
#this begins the model
alpha = pm.Uniform("alpha", 0, 20)
#lets just use uninformative priors
beta = pm.Uniform("beta", 0, 20)
obs = pm.Weibull('obs', alpha, beta, value=lifetime_, observed=True)
@pm.potential
def censor_factor(obs=obs):
if np.any((obs + birth < 10)[lifetime_.mask]):
return -np.inf
else:
return 0
#perform Markov Chain Monte Carlo - see chapter 3 of BMH
The statistical distribution chosen here is the Weibull
distribution, but the same can be done for any other
distribution.
"""
from pymc import rweibull, Uniform, Weibull
"""
First, we will create a fake data set using some
fixed parameters. In real life, of course, you
already have the data !
"""
alpha = 3
beta = 5
N = 100
dataset = rweibull(alpha, beta, N)
"""
Now we create a pymc model that defines the likelihood
of the data set and prior assumptions about the value
of the parameters.
"""
a = Uniform('a', lower=0, upper=10, value=5, doc='Weibull alpha parameter')
b = Uniform('b', lower=0, upper=10, value=5, doc='Weibull beta parameter')
like = Weibull('like', alpha=a, beta=b, value=dataset, observed=True)
pred = Weibull('like', alpha=a, beta=b, value=dataset)
if __name__ == '__main__':
from pymc import MCMC, Matplot
# Sample the parameters a and b and analyze the results
# from pymc.examples import disaster_model
# M = MCMC(disaster_model)
# M.sample(iter=10000, burn=1000, thin=10)
# M.trace('switchpoint')[:]
from pymc import rweibull, Uniform, Weibull
alpha = 3
beta = 5
N = 100
dataset = rweibull(alpha, beta, N)
print dataset
"""
Now we create a pymc model that defines the likelihood
of the data set and prior assumptions about the value
of the parameters.
"""
a = Uniform('a', lower=0, upper=10, value=5, doc='Weibull alpha parameter')
b = Uniform('b', lower=0, upper=10, value=5, doc='Weibull beta parameter')
like = Weibull('like', alpha=a, beta=b, value=dataset, observed=True)
if __name__ == '__main__':
from pymc import MCMC, Matplot
import numpy as np
import matplotlib.pyplot as plt
import pymc as mc
import scipy.stats as stats
import math
# http://blog.yhathq.com/posts/estimating-user-lifetimes-with-pymc.html
# artificial data
N = 20
true_alpha = 2
true_beta = 5
lifetime = mc.rweibull(true_alpha, true_beta, size=N)
birth = mc.runiform(0, 10, N)
# an individual is right censored if this is true
censor = (birth + lifetime) > 10
lifetime_ = np.ma.masked_array(lifetime, censor)
lifetime_.set_fill_value(10)
plt.clf()
y = np.arange(0, N)
for b, l, yy in zip(birth, lifetime, y):
plt.plot([b, b + l], [yy, yy])
plt.plot(birth + lifetime, y, linestyle="", marker="o")
plt.draw()
plt.show(block=False)
# begin the model
# just use uniform priors
alpha = mc.Uniform("alpha", 0, 20)
import pymc
# Some fake data
alpha = 3
beta = 5
N = 100
dataset = pymc.rweibull(alpha, beta, N)
# Model
a = pymc.Uniform('a',
lower=0,
upper=10,
value=5,
doc='Weibull alpha parameter')
b = pymc.Uniform('b', lower=0, upper=10, value=5, doc='Weibull beta parameter')
like = pymc.Weibull('like', alpha=a, beta=b, value=dataset, observed=True)
The statistical distribution chosen here is the Weibull
distribution, but the same can be done for any other
distribution.
"""
import pymc
"""
First, we will create a fake data set using some
fixed parameters. In real life, of course, you
already have the data !
"""
alpha = 3
beta = 5
N = 100
dataset = pymc.rweibull(alpha,beta, N)
"""
Now we create a pymc model that defines the likelihood
of the data set and prior assumptions about the value
of the parameters.
"""
a = pymc.Uniform('a', lower=0, upper=10, value=5, doc='Weibull alpha parameter')
b = pymc.Uniform('b', lower=0, upper=10, value=5, doc='Weibull beta parameter')
like = pymc.Weibull('like', alpha=a, beta=b, value=dataset, observed=True)
"""
The last step is simply to sample the parameters a and b and analyze the
results.
"""
if __name__=='__main__':
import numpy as np
import matplotlib.pyplot as plt
import pymc as mc
import scipy.stats as stats
import math
# http://blog.yhathq.com/posts/estimating-user-lifetimes-with-pymc.html
# artificial data
N = 20
true_alpha = 2
true_beta = 5
lifetime = mc.rweibull( true_alpha, true_beta, size=N )
birth = mc.runiform( 0, 10, N )
# an individual is right censored if this is true
censor = (birth + lifetime) > 10
lifetime_ = np.ma.masked_array( lifetime, censor )
lifetime_.set_fill_value( 10 )
plt.clf()
y = np.arange( 0, N )
for b,l,yy in zip( birth, lifetime, y ):
plt.plot( [b,b+l], [yy,yy] )
plt.plot( birth+lifetime, y, linestyle="", marker="o" )
plt.draw()
plt.show( block=False )
# begin the model
# just use uniform priors
alpha = mc.Uniform( "alpha", 0, 20 )
