#!/usr/bin/env python
# coding: utf-8

# In[2]:


get_ipython().run_line_magic('matplotlib', 'inline')
import pymc3 as pm
import numpy as np
import seaborn as sns


# First, let's run an analysis of 100 binomial samples, with zero positive outcomes:

# In[3]:


n1 = 100
x1 = 0


# In[6]:


with pm.Model() as first_dataset:
    θ = pm.Beta('θ', 1, 1)
    x = pm.Binomial('x', n=n1, p=θ, observed=x1)
    
    trace1 = pm.sample(2000)


# The parameter estimate is 0.012, with a credible interval of length 0.031.

# In[7]:


pm.summary(trace1)


# Now, let's add another 100 samples, but this time with 10 positive outcomes:

# In[8]:


n2 = 100
x2 = 10

with pm.Model() as combined_dataset:
    θ = pm.Beta('θ', 1, 1)
    x = pm.Binomial('x', n=n1+n2, p=θ, observed=x1+x2)
    
    trace2 = pm.sample(2000)


# In[9]:


pm.summary(trace2)


# Notice that the credible interval is twice as large, even with a doubling of the sample size!