In [1]:

    

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


sns.set(font_scale=1.5)


    

In [2]:

    

with pm.Model() as model:
    c_means = pm.Uniform('c_means', 0, 100, shape=5)
    corrections = pm.Normal('corrs', c_means, sd=1, shape=5, observed=[3,4,5,4,3])
    p_means = pm.Uniform('p_means', 0, 100, shape=5)
    p = pm.Poisson('p', p_means, shape=5, observed=[30, 35, 20, 45, 16])
    avg = pm.Deterministic('avg', pm.math.sum(c_means, axis=0) + pm.math.sum(p_means, axis=0)/5)
    
    trace = pm.sample(10000)


    

    




Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [p_means, c_means]
Sampling 2 chains, 0 divergences: 100%|██████████| 21000/21000 [00:12<00:00, 1617.47draws/s]

In [3]:

    

pm.summary(trace)


    

    
Out[3]:







  

    

      

      
mean
      
sd
      
hpd_3%
      
hpd_97%
      
mcse_mean
      
mcse_sd
      
ess_mean
      
ess_sd
      
ess_bulk
      
ess_tail
      
r_hat
    
  
  

    

      
c_means[0]
      
3.013
      
0.981
      
1.083
      
4.793
      
0.007
      
0.005
      
17991.0
      
17991.0
      
17367.0
      
8356.0
      
1.0
    
    

      
c_means[1]
      
3.997
      
0.989
      
2.127
      
5.830
      
0.007
      
0.005
      
21108.0
      
21108.0
      
20809.0
      
10844.0
      
1.0
    
    

      
c_means[2]
      
5.000
      
1.006
      
3.148
      
6.914
      
0.006
      
0.005
      
24783.0
      
24783.0
      
24903.0
      
11266.0
      
1.0
    
    

      
c_means[3]
      
4.002
      
1.009
      
2.122
      
5.904
      
0.007
      
0.005
      
23110.0
      
23110.0
      
23302.0
      
10057.0
      
1.0
    
    

      
c_means[4]
      
3.008
      
0.987
      
1.142
      
4.839
      
0.007
      
0.005
      
20088.0
      
20088.0
      
19526.0
      
10649.0
      
1.0
    
    

      
p_means[0]
      
30.958
      
5.532
      
21.147
      
41.582
      
0.033
      
0.024
      
27546.0
      
25524.0
      
27984.0
      
14584.0
      
1.0
    
    

      
p_means[1]
      
36.014
      
5.992
      
25.148
      
47.323
      
0.036
      
0.027
      
27775.0
      
25399.0
      
28560.0
      
14025.0
      
1.0
    
    

      
p_means[2]
      
21.028
      
4.580
      
12.783
      
29.626
      
0.026
      
0.020
      
30479.0
      
26678.0
      
31297.0
      
14131.0
      
1.0
    
    

      
p_means[3]
      
45.977
      
6.881
      
33.130
      
58.873
      
0.042
      
0.031
      
27470.0
      
24821.0
      
28676.0
      
12313.0
      
1.0
    
    

      
p_means[4]
      
16.986
      
4.167
      
9.177
      
24.567
      
0.024
      
0.018
      
29977.0
      
26330.0
      
30326.0
      
13785.0
      
1.0
    
    

      
avg
      
49.212
      
3.332
      
43.048
      
55.576
      
0.021
      
0.015
      
25465.0
      
25224.0
      
25513.0
      
15294.0
      
1.0
    
  

In [4]:

    

pm.traceplot(trace)


    

    




/Users/balarsen/miniconda3/envs/python3/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/distplot.py:38: UserWarning: Argument backend_kwargs has not effect in matplotlib.plot_distSupplied value won't be used
  "Argument backend_kwargs has not effect in matplotlib.plot_dist"
/Users/balarsen/miniconda3/envs/python3/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/distplot.py:38: UserWarning: Argument backend_kwargs has not effect in matplotlib.plot_distSupplied value won't be used
  "Argument backend_kwargs has not effect in matplotlib.plot_dist"
/Users/balarsen/miniconda3/envs/python3/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/distplot.py:38: UserWarning: Argument backend_kwargs has not effect in matplotlib.plot_distSupplied value won't be used
  "Argument backend_kwargs has not effect in matplotlib.plot_dist"






    
Out[4]:





array([[<matplotlib.axes._subplots.AxesSubplot object at 0x1285ae6d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x129128dd0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x129654b50>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12968d910>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1296c6bd0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1296fec10>]],
      dtype=object)






    

In [5]:

    

pm.plot_posterior(trace)


    

    
Out[5]:





array([<matplotlib.axes._subplots.AxesSubplot object at 0x12a4ebad0>,
       <matplotlib.axes._subplots.AxesSubplot object at 0x12a5bb850>,
       <matplotlib.axes._subplots.AxesSubplot object at 0x12a5f4890>],
      dtype=object)






    

In [6]:

    

print(np.average([30, 35, 20, 45, 16]))


    

    




29.2

In [12]:

    

with pm.Model() as model:
    p_means = pm.Uniform('p_means', 0, 100, shape=(5, 16))  # time, pixel, sector
    p = pm.Poisson('p', p_means, shape=5, observed=np.random.poisson(30, size=(5, 16)))
    avg = pm.Deterministic('avg', pm.math.sum(p_means)/(5*16))
    
    trace = pm.sample(10000)


    

    




INFO (theano.gof.compilelock): Refreshing lock /Users/balarsen/.theano/compiledir_Darwin-18.7.0-x86_64-i386-64bit-i386-3.7.6-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [p_means]
Sampling 2 chains, 0 divergences: 100%|██████████| 21000/21000 [00:11<00:00, 1892.77draws/s]

In [13]:

    

pm.summary(trace)


    

    
Out[13]:







  

    

      

      
mean
      
sd
      
hpd_3%
      
hpd_97%
      
mcse_mean
      
mcse_sd
      
ess_mean
      
ess_sd
      
ess_bulk
      
ess_tail
      
r_hat
    
  
  

    

      
p_means[0,0]
      
31.019
      
5.606
      
20.973
      
41.886
      
0.029
      
0.022
      
36484.0
      
31995.0
      
37615.0
      
13528.0
      
1.0
    
    

      
p_means[0,1]
      
28.996
      
5.423
      
18.878
      
38.954
      
0.031
      
0.023
      
30850.0
      
27753.0
      
31984.0
      
15189.0
      
1.0
    
    

      
p_means[0,2]
      
34.018
      
5.821
      
23.702
      
45.180
      
0.030
      
0.023
      
37132.0
      
31559.0
      
39285.0
      
13392.0
      
1.0
    
    

      
p_means[0,3]
      
30.992
      
5.596
      
20.520
      
41.353
      
0.032
      
0.024
      
31291.0
      
27784.0
      
32416.0
      
13568.0
      
1.0
    
    

      
p_means[0,4]
      
25.959
      
5.054
      
17.050
      
35.843
      
0.027
      
0.020
      
35055.0
      
30526.0
      
36394.0
      
14481.0
      
1.0
    
    

      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
      
...
    
    

      
p_means[4,12]
      
33.979
      
5.854
      
23.257
      
44.853
      
0.031
      
0.023
      
36571.0
      
32177.0
      
37791.0
      
13523.0
      
1.0
    
    

      
p_means[4,13]
      
28.967
      
5.379
      
19.189
      
39.285
      
0.027
      
0.021
      
39670.0
      
33861.0
      
40855.0
      
12167.0
      
1.0
    
    

      
p_means[4,14]
      
30.939
      
5.483
      
20.897
      
41.374
      
0.028
      
0.021
      
37143.0
      
32625.0
      
38408.0
      
14148.0
      
1.0
    
    

      
p_means[4,15]
      
32.014
      
5.639
      
21.755
      
42.671
      
0.031
      
0.023
      
34111.0
      
29706.0
      
35870.0
      
14018.0
      
1.0
    
    

      
avg
      
31.309
      
0.621
      
30.171
      
32.494
      
0.003
      
0.002
      
35823.0
      
35823.0
      
35773.0
      
14234.0
      
1.0
    
  

81 rows × 11 columns

In [14]:

    

pm.traceplot(trace)


    

    




/Users/balarsen/miniconda3/envs/python3/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/distplot.py:38: UserWarning: Argument backend_kwargs has not effect in matplotlib.plot_distSupplied value won't be used
  "Argument backend_kwargs has not effect in matplotlib.plot_dist"
/Users/balarsen/miniconda3/envs/python3/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/distplot.py:38: UserWarning: Argument backend_kwargs has not effect in matplotlib.plot_distSupplied value won't be used
  "Argument backend_kwargs has not effect in matplotlib.plot_dist"






    
Out[14]:





array([[<matplotlib.axes._subplots.AxesSubplot object at 0x133c4d710>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x131d6c6d0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x129e9c710>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12adc0a50>]],
      dtype=object)






    

In [15]:

    

pm.plot_posterior(trace)


    

    
Out[15]:





array([<matplotlib.axes._subplots.AxesSubplot object at 0x128799a50>,
       <matplotlib.axes._subplots.AxesSubplot object at 0x1283f5690>],
      dtype=object)






    

In [ ]: