Title :¶

Bayes - Exercise 2

Description :¶

Model $y$ as a least-squares regression as $y = \alpha + \beta \cdot x + \epsilon$

After completing this exercise you should see following trace plots:

Hints:¶

pymc3 Normal

Refer to lecture notebook.

Do not change any other code except the blanks.

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!pip install xarray==0.16.0

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import pandas as pd
import numpy as np

import pymc3 as pm

from matplotlib import pyplot
%matplotlib inline

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df = pd.read_csv('data3.csv')

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### edTest(test_pm_model) ###
np.random.seed(109)
with pm.Model() as model:
    # prior
    alpha = pm.Normal('alpha', mu=0, tau=1000)
    beta = pm.Normal('beta', mu=0, tau=1000)
    
    # likelihood
    # Next statement creates the expected value of mu_vec of the 
    # outcomes, specifying the linear relationship.
    # mu_vec is just the sum of the intercept alpha and the product of
    # the coefficient  beta and the predictor variable. 
    mu_vec = pm.Deterministic('mu_vec', ____)
    
    tau_obs = pm.Gamma('tau_obs', 0.001, 0.001)
    obs = pm.Normal(_______)  #Parameters to set: name, mu, tau, observed
    trace = pm.sample(2000, tune=2000, chains=2)
    pm.traceplot(trace, var_names=['alpha','beta','tau_obs'], compact=False);

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#posterior means
np.mean(trace['alpha']),np.mean(trace['beta']), np.mean(trace['tau_obs'])

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