buck-evan.ipynb

Kernel: Environment (conda_bayesian)

import pymc3 as pm
import numpy as np
import matplotlib.pyplot as plt


%load_ext autoreload
%autoreload 2
%matplotlib inline
%config InlineBackend.figure_format = 'retina'

# Data
k_known = 30
theta_known = 5
alpha_known = k_known
beta_known = 1 / theta_known
data_sample_size = 5
data = np.random.gamma(shape=k_known, scale=theta_known, size=data_sample_size)
data

full_distribution = np.random.gamma(k_known, theta_known, size=10000)
plt.hist(full_distribution)

with pm.Model() as buck_problem:
    k = pm.HalfCauchy("k", 100 ** 2)
    # theta = pm.HalfCauchy('theta', 100**2)

    beta = pm.HalfCauchy("beta", 100 ** 2)
    likelihood = pm.Gamma("like", alpha=k, beta=beta, observed=data)
    theta = pm.Deterministic("theta", 1 / beta)

with buck_problem:
    trace = pm.sample(10000)

with buck_problem:
    pm.traceplot(trace[1000:])

with buck_problem:
    pm.plot_posterior(trace[1000:])

plt.scatter(trace["k"], trace["theta"])

import seaborn as sns

sns.jointplot(trace["k"], trace["theta"])