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# Import relevant modules
import pymc
import numpy as np
import matplotlib.pyplot as plt


    

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# Some data
n = 5 * np.ones(4, dtype=int)
x = np.array([-.86, -.3, -.05, .73])


    

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# Priors on unknown parameters
alpha = pymc.Normal('alpha', mu=0, tau=.01)
beta = pymc.Normal('beta', mu=0, tau=.01)

# Arbitrary deterministic function of parameters
@pymc.deterministic
def theta(a=alpha, b=beta):
    """theta = logit^{-1}(a+b)"""
    return pymc.invlogit(a + b * x)

# Binomial likelihood for data
d = pymc.Binomial('d', n=n, p=theta, value=np.array([0., 1., 3., 5.]),
                  observed=True)


    

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mymodel = pymc.Model([theta, d])
S = pymc.MCMC(mymodel, db='pickle')


    

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S.sample(iter=10000, burn=5000, thin=2)


    

    




 [-----------------100%-----------------] 10000 of 10000 complete in 0.3 sec

In [11]:

    

pymc.Matplot.plot(S)


    

    




Plotting theta_0
Plotting theta_1
Plotting theta_2
Plotting theta_3

In [12]:

    

plt.show()


    

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