In [2]:

    

%matplotlib inline

from pymc3 import  *

import numpy as np
import matplotlib.pyplot as plt
import seaborn


    

In [3]:

    

size = 200
true_intercept = 1
true_slope = 2

x = np.linspace(0, 1, size)
# y = a + b*x
true_regression_line = true_intercept + true_slope * x
# add noise
y = true_regression_line + np.random.normal(scale=.5, size=size)

data = dict(x=x, y=y)


    

In [19]:

    

fig = plt.figure(figsize=(7, 7))
ax = fig.add_subplot(111, xlabel='x', ylabel='y', title='Generated data and underlying model')
ax.plot(x, y, '*b', label='sampled data')
ax.plot(x, true_regression_line, 'g', label='true regression line', lw=2.)
plt.legend(loc=0)


    

    
Out[19]:





<matplotlib.legend.Legend at 0x10eb14c50>






    

In [22]:

    

with Model() as model:
    glm.glm('y ~ x', data)
    start = find_MAP()
    step = NUTS(scaling=start)
    trace = sample(10000, step)


    

    




 [-----------------100%-----------------] 10000 of 10000 complete in 16.1 sec

In [25]:

    

traceplot(trace[1000:])


    

    
Out[25]:





array([[<matplotlib.axes._subplots.AxesSubplot object at 0x118b404d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x119055a10>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x105d68850>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x119156cd0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1191d9b10>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x11917a510>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1192cb910>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x119350650>]], dtype=object)






    

In [35]:

    

plt.figure(figsize=(7, 7))
plt.plot(x, y, '*b', label='data')
glm.plot_posterior_predictive(trace, samples=50, 
                              label='posterior predictive regression lines')
plt.plot(x, true_regression_line, label='true regression line', lw=2., c='g')

plt.title('Posterior predictive regression lines')
plt.legend(loc=0)
plt.xlabel('x')
plt.ylabel('y')


    

    
Out[35]:





<matplotlib.text.Text at 0x11a96c110>






    

In [ ]: