"""
from __future__ import division
import numpy as np
import pymc3 as pm
import matplotlib.pyplot as plt
from plot_post import plot_post
## specify the Data
y = np.repeat([0, 1], [3, 6]) # 3 tails 6 heads
with pm.Model() as model:
# Hyperhyperprior:
model_index = pm.DiscreteUniform('model_index', lower=0, upper=1)
# Hyperprior:
kappa_theta = 12
mu_theta = pm.switch(pm.eq(model_index, 1), 0.25, 0.75)
# Prior distribution:
a_theta = mu_theta * kappa_theta
b_theta = (1 - mu_theta) * kappa_theta
theta = pm.Beta('theta', a_theta,
b_theta) # theta distributed as beta density
#likelihood
y = pm.Bernoulli('y', theta, observed=y)
start = pm.find_MAP()
step = pm.Metropolis()
trace = pm.sample(10000, step, start=start, progressbar=False)
## Check the results.
burnin = 2000 # posterior samples to discard
thin = 1 # posterior samples to discard
# Hyperprior on mu and kappa:
kappa = pm.Gamma('kappa', shape_Gamma, rate_Gamma, shape=n_cond)
mu0 = pm.Beta('mu0', 1, 1)
a_Beta0 = mu0 * kappa[cond_of_subj]
b_Beta0 = (1 - mu0) * kappa[cond_of_subj]
mu1 = pm.Beta('mu1', 1, 1, shape=n_cond)
a_Beta1 = mu1[cond_of_subj] * kappa[cond_of_subj]
b_Beta1 = (1 - mu1[cond_of_subj]) * kappa[cond_of_subj]
#Prior on theta
theta0 = pm.Beta('theta0', a_Beta0, b_Beta0, shape=n_subj)
theta1 = pm.Beta('theta1', a_Beta1, b_Beta1, shape=n_subj)
# if model_index == 0 then sample from theta1 else sample from theta0
theta = pm.switch(pm.eq(model_index, 0), theta1, theta0)
# Likelihood:
y = pm.Binomial('y', p=theta, n=n_trl_of_subj, observed=n_corr_of_subj)
# Sampling
start = pm.find_MAP()
step1 = pm.Metropolis(model.vars[1:])
step2 = pm.ElemwiseCategoricalStep(var=model_index,values=[0,1])
trace = pm.sample(20000, [step1, step2], start=start, progressbar=False)
# EXAMINE THE RESULTS.
burnin = 10000
thin = 10
# 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()
step1 = pm.Metropolis(model.vars[1:])
step2 = pm.ElemwiseCategoricalStep(var=model_index, values=[0, 1])
trace = pm.sample(10000, [step1, step2], start=start, progressbar=False)
# EXAMINE THE RESULTS.
burnin = 1000
thin = 5
## Print summary for each trace
#pm.summary(trace[burnin::thin])
#pm.summary(trace)
"""
from __future__ import division
import numpy as np
import pymc3 as pm
import matplotlib.pyplot as plt
from plot_post import plot_post
## specify the Data
y = np.repeat([0, 1], [3, 6]) # 3 tails 6 heads
with pm.Model() as model:
# Hyperhyperprior:
model_index = pm.DiscreteUniform('model_index', lower=0, upper=1)
# Hyperprior:
kappa_theta = 12
mu_theta = pm.switch(pm.eq(model_index, 1), 0.25, 0.75)
# Prior distribution:
a_theta = mu_theta * kappa_theta
b_theta = (1 - mu_theta) * kappa_theta
theta = pm.Beta('theta', a_theta, b_theta) # theta distributed as beta density
#likelihood
y = pm.Bernoulli('y', theta, observed=y)
start = pm.find_MAP()
step = pm.Metropolis()
trace = pm.sample(10000, step, start=start, progressbar=False)
## Check the results.
burnin = 2000 # posterior samples to discard
thin = 1 # posterior samples to discard
