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10_ToyModelCompPyMC.py
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10_ToyModelCompPyMC.py
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"""
Comparing models using Hierarchical modelling. Toy Model.
"""
from __future__ import division
import numpy as np
import pymc as pm
import matplotlib.pyplot as plt
from plot_post import plot_post
# THE DATA.
N = 30
z = 8
y = np.repeat([1, 0], [z, N-z])
# THE MODEL.
with pm.Model() as model:
# Hyperprior on model index:
model_index = pm.DiscreteUniform('model_index', lower=0, upper=1)
# Prior
nu = pm.Normal('nu', mu=0, tau=0.1) # it is posible to use tau or sd
eta = pm.Gamma('eta', .1, .1)
theta0 = 1 / (1 + pm.exp(-nu)) # theta from model index 0
theta1 = pm.exp(-eta) # theta from model index 1
theta = pm.switch(pm.eq(model_index, 0), theta0, theta1)
# Likelihood
y = pm.Bernoulli('y', p=theta, observed=y)
# Sampling
start = pm.find_MAP()
steps = [pm.Metropolis([i]) for i in model.unobserved_RVs[1:]]
steps.append(pm.ElemwiseCategoricalStep(var=model_index,values=[0,1]))
trace = pm.sample(10000, steps, start=start, progressbar=False)
# EXAMINE THE RESULTS.
burnin = 1000
thin = 5
## Print summary for each trace
#pm.summary(trace[burnin::thin])
#pm.summary(trace)
## Check for mixing and autocorrelation
#pm.autocorrplot(trace[burnin::thin], vars =[nu, eta])
#pm.autocorrplot(trace, vars =[nu, eta])
## Plot KDE and sampled values for each parameter.
#pm.traceplot(trace[burnin::thin])
#pm.traceplot(trace)
model_idx_sample = trace['model_index'][burnin::thin]
pM1 = sum(model_idx_sample == 0) / len(model_idx_sample)
pM2 = 1 - pM1
nu_sample_M1 = trace['nu'][burnin::thin][model_idx_sample == 0]
eta_sample_M2 = trace['eta'][burnin::thin][model_idx_sample == 1]
plt.figure()
plt.subplot(2, 1, 1)
plot_post(nu_sample_M1, xlab=r'$\nu$', show_mode=False, labelsize=9, framealpha=0.5)
plt.xlabel(r'$\nu$')
plt.ylabel('frequency')
plt.title(r'p($\nu$|D,M2), with p(M2|D)=%.3f' % pM1, fontsize=14)
plt.xlim(-8, 8)
plt.subplot(2, 1, 2)
plot_post(eta_sample_M2, xlab=r'$\eta$', show_mode=False, labelsize=9, framealpha=0.5)
plt.xlabel(r'$\eta$')
plt.ylabel('frequency')
plt.title(r'p($\eta$|D,M2), with p(M2|D)=%.3f' % pM2, fontsize=14)
plt.xlim(0, 8)
plt.savefig('figure_ex_10.2_a.png')
plt.show()