Likelihood-ratio test

In [4]:

    

import numpy as np
import scipy
import seaborn as sns
import pymc3 as pm
import matplotlib.pyplot as plt

sns.set(font_scale=1.5)


    

In [6]:

    

data_dist = scipy.stats.beta(2, 5)


    

In [7]:

    

XX = np.linspace(0, 1, 100)
plt.plot(XX, data_dist.pdf(XX))


    

    
Out[7]:





[<matplotlib.lines.Line2D at 0x120039080>]






    

In [8]:

    

data = data_dist.rvs(size=100)


    

In [9]:

    

sns.distplot(data)


    

    
Out[9]:





<matplotlib.axes._subplots.AxesSubplot at 0x120d8b358>






    

In [17]:

    

with pm.Model() as model:
    n_mu = pm.Uniform('n_mu', 0, 100)
    n_sd = pm.Uniform('n_sd', 0, 100)
    normal = pm.Normal('normal', n_mu, sd=n_sd, observed=data)
    
    b_alpha = pm.Uniform('b_alpha', 0, 100)
    b_beta = pm.Uniform('b_beta', 0, 100)
    beta = pm.Beta('beta', b_alpha, b_beta, observed=data)

    trace = pm.sample(10000)


    

    




Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [b_beta, b_alpha, n_sd, n_mu]
Sampling 4 chains: 100%|██████████| 42000/42000 [00:19<00:00, 2182.09draws/s]

In [18]:

    

pm.traceplot(trace, combined=True)


    

    
Out[18]:





array([[<matplotlib.axes._subplots.AxesSubplot object at 0x124d1c3c8>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12644e828>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x126433f98>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1263d3208>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1263c0a58>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12638eeb8>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x126342f60>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1262c7b70>]],
      dtype=object)






    

In [19]:

    

ppc = pm.sample_posterior_predictive(trace, samples=5000, model=model)


    

    




100%|██████████| 5000/5000 [00:04<00:00, 1031.56it/s]

In [35]:

    

plt.figure(figsize=(10,6))
sns.kdeplot(ppc['normal'].flatten(), label='normal', lw=3)
sns.kdeplot(ppc['beta'].flatten(), label='beta', lw=3)
sns.distplot(data, label='data')
plt.legend()


    

    
Out[35]:





<matplotlib.legend.Legend at 0x12528b400>






    

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