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

# In[1]:


get_ipython().run_line_magic('load_ext', 'autoreload')
get_ipython().run_line_magic('autoreload', '2')


# In[2]:


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


# In[3]:


t_data = pm.StudentT.dist(nu=5).random(size=1000)
sns.distplot(t_data, kde=False);


# Using the Student-T directly

# In[4]:


with pm.Model() as m0:
    ν = pm.HalfNormal('ν', sigma=5)
    t = pm.StudentT('t', nu=ν, observed=t_data)
    
    trace0 = pm.sample(1000, tune=2000, cores=2)


# In[5]:


az.plot_trace(trace0);


# In[6]:


with pm.Model() as m1:
    ν = pm.HalfNormal('ν', sigma=5)
    σ2 = pm.InverseGamma('σ2', alpha=ν/2, beta=ν/2, shape=len(t_data))
    t = pm.Normal('t', sigma=pm.math.sqrt(σ2), observed=t_data)
    
    trace1 = pm.sample(1000, tune=1000, cores=2)


# In[7]:


az.plot_trace(trace1, var_names=['ν']);