Make a custom distribution from the logp functions, compare to real one

In [15]:

    

import itertools

import arviz as az
import matplotlib.pyplot as plt
import matplotlib as mpl
import pymc3 as pm
from pymc3 import Model, Normal, Slice
from pymc3 import sample
from pymc3 import traceplot
from pymc3.distributions import Interpolated
from theano import as_op
import theano.tensor as tt
import numpy as np
from scipy import stats
import scipy
import tqdm
import pandas as pd

%matplotlib inline

%load_ext version_information

%version_information pymc3, scipy


    

    




The version_information extension is already loaded. To reload it, use:
  %reload_ext version_information






    
Out[15]:




Software
Version
Python
3.7.3 64bit [Clang 4.0.1 (tags/RELEASE_401/final)]
IPython
7.5.0
OS
Darwin 18.6.0 x86_64 i386 64bit
pymc3
3.7
scipy
1.3.0
Tue Jun 04 16:47:41 2019 MDT

In [19]:

    

with pm.Model() as model:
    def logp_poi(k):
        return np.log(lam**k*np.exp(-lam)/scipy.special.factorial(k))
    
    
    
    poi = pm.Poisson('poi', 100)
    poi_custom = pm.DensityDist('poi_custom', logp_exp, )

    trace = pm.sample(10000)


    

    




Multiprocess sampling (4 chains in 4 jobs)
CompoundStep
>Metropolis: [poi]
>NUTS: [poi_custom]
Sampling 4 chains: 100%|██████████| 42000/42000 [00:09<00:00, 4406.34draws/s]
There were 1188 divergences after tuning. Increase `target_accept` or reparameterize.
The acceptance probability does not match the target. It is 0.0072562193308475745, but should be close to 0.8. Try to increase the number of tuning steps.
There were 1163 divergences after tuning. Increase `target_accept` or reparameterize.
The acceptance probability does not match the target. It is 0.009999136353924765, but should be close to 0.8. Try to increase the number of tuning steps.
There were 1238 divergences after tuning. Increase `target_accept` or reparameterize.
The acceptance probability does not match the target. It is 0.00673795472584753, but should be close to 0.8. Try to increase the number of tuning steps.
There were 1178 divergences after tuning. Increase `target_accept` or reparameterize.
The acceptance probability does not match the target. It is 0.009816872184785176, but should be close to 0.8. Try to increase the number of tuning steps.
The gelman-rubin statistic is larger than 1.4 for some parameters. The sampler did not converge.
The estimated number of effective samples is smaller than 200 for some parameters.

In [21]:

    

az.plot_trace(trace, combined=True)


    

    
Out[21]:





array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7ff0c9b2e1d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x7ff0c9e43dd8>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x7ff10b6cfbe0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x7ff0c9e52e80>]],
      dtype=object)






    

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