# 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)
## 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.
# cluster centers
means = pm.Normal('means', mu=[0, 0, 0], sd=15, shape=k)
# break symmetry
order_means_potential = pm.Potential('order_means_potential',
tt.switch(np.dot(means[1]-means[0], np.transpose(means[1]-means[0])) < 0, -np.inf, 0)
+ tt.switch(means[2]-means[1] < 0, -np.inf, 0))
# measurement error
sd = pm.Uniform('sd', lower=0, upper=20)
# latent cluster of each observation
category = pm.Categorical('category',
p=p,
shape=ndata)
# likelihood for each observed value
points = pm.Normal('obs',
mu=means[category],
sd=sd,
observed=data)
with model:
step1 = pm.Metropolis(vars=[p, sd, means])
step2 = pm.ElemwiseCategoricalStep(vars=[category], values=[0, 1, 2])
tr = pm.sample(10000, step=[step1, step2])
pm.plots.traceplot(tr, ['p', 'sd', 'means'])
# plt.hist(data)
plt.show()
a_Beta1 = mu[cond_of_subj] * kappa1[cond_of_subj]
b_Beta1 = (1 - mu[cond_of_subj]) * kappa1[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()
steps = [pm.Metropolis([i]) for i in model.unobserved_RVs[1:]]
steps.append(pm.ElemwiseCategoricalStep(var=model_index, values=[0, 1]))
trace = pm.sample(50000, steps, start=start, progressbar=False)
# EXAMINE THE RESULTS.
burnin = 1000
thin = 1
model_idx_sample = trace['model_index'][burnin::thin]
pM1 = sum(model_idx_sample == 1) / len(model_idx_sample)
pM2 = 1 - pM1
plt.figure(figsize=(15, 15))
plt.subplot2grid((5, 4), (0, 0), colspan=4)
plt.plot(model_idx_sample,
label='p(M1|D) = %.3f ; p(M2|D) = %.3f' % (pM1, pM2))
plt.xlabel('Step in Markov Chain')
# for (i in 1:m){
# k[i] ~ dbin(theta,n)
# }
# # Priors on Rate Theta and Number n
# theta ~ dbeta(1,1)
# n ~ dcat(p[])
# for (i in 1:nmax){
# p[i] <- 1/nmax
# }
#}
with model:
# Priors on rate theta and number n
theta = pm.Beta('theta', alpha=1, beta=1)
p = pm.constant(np.ones(nmax) / nmax)
n = pm.Categorical('n', p=p, shape=1) #FIXME: How to use this properly?
# Observed Returns
# k = pm.Binomial('k', p=theta, n=n, observed=k, shape=m)
# instantiate samplers
values_np = np.ones(nmax) / nmax #FIXME: How to use this properly?
step1 = pm.Metropolis([theta])
step2 = pm.ElemwiseCategoricalStep(var=n, values=values_np)
stepFunc = [step1, step2]
# draw posterior samples (in 4 parallel running chains), TODO: very slow!?
Nsample = 100
Nchains = 4
traces = pm.sample(Nsample, step=stepFunc, njobs=Nchains)
plotVars = ['theta', 'n']
axs = pm.traceplot(traces, vars=plotVars, combined=False)
axs[0][0].set_xlim([0, 1]) # manually set x-limits for comparisons