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

# In[13]:


get_ipython().run_line_magic('matplotlib', 'inline')
from pymc3 import Normal, sample, Model, traceplot, plots, Metropolis, Potential, variational, HalfCauchy,summary
from theano import scan, shared
from scipy import optimize
import theano.tensor as tt
import matplotlib.pyplot as plt

import numpy as np


# In[2]:


y = shared(np.array([15, 10, 16, 11, 9, 11, 10, 18], dtype=np.float32))


# In[3]:


with Model() as arma_model:

    sigma = HalfCauchy('sigma', 5)
    theta = Normal('theta', 0, sd=2)
    phi = Normal('phi', 0, sd=2)
    mu = Normal('mu', 0, sd=10)

    err0 = y[0] - (mu + phi*mu)
                                 
    def calc_next(last_y, this_y, err, mu, phi, theta):
        nu_t = mu + phi*last_y + theta*err
        return this_y - nu_t
        
    err, _ = scan(fn=calc_next,
                  sequences=dict(input=y, taps=[-1,0]),
                  outputs_info=[err0],
                  non_sequences=[mu, phi, theta])
                  
    like = Potential('like', Normal.dist(0, sd=sigma).logp(err))


# In[15]:


with arma_model:
    trace = sample(2000)


# In[16]:


traceplot(trace[1000:]);