TruncatedNormal

In [1]:

    

import matplotlib.pyplot as plt
import numpy as np
from scipy import stats
import seaborn as sns
import pymc3 as pm
import pandas as pd

%matplotlib inline
sns.set(font_scale=1.5)


    

In [8]:

    

data = np.random.normal(2, 2, size=20)
data = data[data > 0]
data


    

    
Out[8]:





array([0.14568013, 2.54837666, 0.77564356, 0.2037265 , 1.36044847,
       2.49665803, 0.80871428, 2.05183848, 3.00514862, 1.66909572,
       3.0813126 , 1.45238379, 1.16459861, 1.73612704, 1.22713344,
       6.56894626, 2.15293012, 1.71000748, 1.32382677])

In [9]:

    

sns.distplot(data)


    

    
Out[9]:





<matplotlib.axes._subplots.AxesSubplot at 0x1c2576d0d0>






    

In [11]:

    

with pm.Model() as model:
    mean = pm.Uniform('mean', 0, 100)
    sd = pm.Uniform('sd', 0, 100)
    norm = pm.TruncatedNormal('norm', mu=mean, sigma=sd, lower=0)
    trace = pm.sample(1000)


    

    




Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [norm, sd, mean]
Sampling 2 chains: 100%|██████████| 3000/3000 [00:02<00:00, 1054.77draws/s]
There were 111 divergences after tuning. Increase `target_accept` or reparameterize.
There were 81 divergences after tuning. Increase `target_accept` or reparameterize.
The acceptance probability does not match the target. It is 0.7193673915433556, but should be close to 0.8. Try to increase the number of tuning steps.
The estimated number of effective samples is smaller than 200 for some parameters.

In [12]:

    

pm.traceplot(trace)


    

    
Out[12]:





array([[<matplotlib.axes._subplots.AxesSubplot object at 0x1c29f03990>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x111629690>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1c26042950>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1c26069dd0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1c26098650>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1c260cc910>]],
      dtype=object)






    

In [22]:

    

with pm.Model() as model:
    mean = pm.Uniform('mean', 0, 100)
    sd = pm.Uniform('sd', 0, 100)
    norm = pm.TruncatedNormal('norm', mu=mean, sigma=sd, lower=0, observed=data+10)
    trace = pm.sample(5000, tune=1000, target_accept=0.9)


    

    




Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [sd, mean]
Sampling 2 chains: 100%|██████████| 12000/12000 [00:06<00:00, 1956.53draws/s]

In [23]:

    

pm.traceplot(trace)


    

    
Out[23]:





array([[<matplotlib.axes._subplots.AxesSubplot object at 0x1c2a4781d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1c2f9b57d0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1c2f92fe90>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1c2f8f94d0>]],
      dtype=object)






    

In [31]:

    

trace.get_values('mean')


    

    
Out[31]:





array([12.05673274, 11.67734871, 12.04520494, ..., 11.48027536,
       12.008448  , 11.14983553])

In [33]:

    

sns.distplot(trace.get_values('mean')-10)


    

    
Out[33]:





<matplotlib.axes._subplots.AxesSubplot at 0x1c2fbdacd0>






    

In [34]:

    

pm.summary(trace)


    

    




/Users/balarsen/miniconda3/envs/python3/lib/python3.7/site-packages/pymc3/stats.py:991: FutureWarning: The join_axes-keyword is deprecated. Use .reindex or .reindex_like on the result to achieve the same functionality.
  axis=1, join_axes=[dforg.index])






    
Out[34]:







  

    

      

      
mean
      
sd
      
mc_error
      
hpd_2.5
      
hpd_97.5
      
n_eff
      
Rhat
    
  
  

    

      
mean
      
11.869117
      
0.350850
      
0.003859
      
11.126730
      
12.524384
      
6677.368375
      
0.999928
    
    

      
sd
      
1.515014
      
0.279144
      
0.003222
      
1.047906
      
2.084130
      
6297.734771
      
0.999980
    
  

In [35]:

    

pm.plot_posterior(trace)


    

    
Out[35]:





array([<matplotlib.axes._subplots.AxesSubplot object at 0x1c30387e10>,
       <matplotlib.axes._subplots.AxesSubplot object at 0x1c307bbd50>],
      dtype=object)






    

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