def bayesian_random_effects(data, labels, group, n_samples=2000, n_burnin=500):
import pymc as pm
#preparing the data
donors = data[group].unique()
donors_lookup = dict(zip(donors, range(len(donors))))
data['donor_code'] = data[group].replace(donors_lookup).values
n_donors = len(data[group].unique())
donor_idx = data['donor_code'].values
#setting up the model
with pm.Model() as hierarchical_model:
# Hyperpriors for group nodes
group_intercept_mean = pm.Normal('group intercept (mean)', mu=0., sd=100**2)
group_intercept_variance = pm.Uniform('group intercept (variance)', lower=0, upper=100)
group_slope_mean = pm.Normal('group slope (mean)', mu=0., sd=100**2)
group_slope_variance = pm.Uniform('group slope (variance)', lower=0, upper=100)
individual_intercepts = pm.Normal('individual intercepts', mu=group_intercept_mean, sd=group_intercept_variance, shape=n_donors)
individual_slopes = pm.Normal('individual slopes', mu=group_slope_mean, sd=group_slope_variance, shape=n_donors)
# Model error
residuals = pm.Uniform('residuals', lower=0, upper=100)
expression_est = individual_slopes[donor_idx] * data[labels[0]].values + individual_intercepts[donor_idx]
# Data likelihood
expression_like = pm.Normal('expression_like', mu=expression_est, sd=residuals, observed=data[labels[1]])
start = pm.find_MAP()
step = pm.NUTS(scaling=start)
hierarchical_trace = pm.sample(n_samples, step, start=start, progressbar=True)
mean_slope = hierarchical_trace['group slope (mean)'][n_burnin:].mean()
zero_percentile = percentileofscore(hierarchical_trace['group slope (mean)'][n_burnin:], 0)
print "Mean group level slope was %g (zero was %g percentile of the posterior distribution)"%(mean_slope, zero_percentile)
pm.summary(hierarchical_trace[n_burnin:], vars=['group slope (mean)'])
pm.traceplot(hierarchical_trace[n_burnin:])
selection = donors
fig, axis = plt.subplots(2, 3, figsize=(12, 6), sharey=True, sharex=True)
axis = axis.ravel()
xvals = np.linspace(data[labels[0]].min(), data[labels[0]].max())
for i, c in enumerate(selection):
c_data = data.ix[data[group] == c]
c_data = c_data.reset_index(drop = True)
z = list(c_data['donor_code'])[0]
for a_val, b_val in zip(hierarchical_trace['individual intercepts'][n_burnin::10][z], hierarchical_trace['individual slopes'][n_burnin::10][z]):
axis[i].plot(xvals, a_val + b_val * xvals, 'g', alpha=.1)
axis[i].plot(xvals, hierarchical_trace['individual intercepts'][n_burnin:][z].mean() + hierarchical_trace['individual slopes'][n_burnin:][z].mean() * xvals,
'g', alpha=1, lw=2.)
axis[i].hexbin(c_data[labels[0]], c_data[labels[1]], mincnt=1, cmap=plt.cm.YlOrRd_r)
axis[i].set_title(c)
axis[i].set_xlabel(labels[0])
axis[i].set_ylabel(labels[1])
plt.show()
return mean_slope, zero_percentile
def test_summary_2d_variable_model():
mu = -2.1
tau = 1.3
with Model() as model:
x = Normal('x', mu, tau, shape=(2, 2), testval=np.tile(.1, (2, 2)))
step = Metropolis(model.vars, np.diag([1.]), blocked=True)
trace = pm.sample(100, step=step)
pm.summary(trace)
def test_summary_1d_variable_model():
mu = -2.1
tau = 1.3
with Model() as model:
x = Normal('x', mu, tau, shape=2, testval=[.1, .1])
step = Metropolis(model.vars, np.diag([1.]))
trace = pm.sample(100, step=step)
pm.summary(trace)
def test_summary_1_value_model():
mu = -2.1
tau = 1.3
with Model() as model:
x = Normal('x', mu, tau, testval=.1)
step = Metropolis(model.vars, np.diag([1.]))
trace = sample(100, step=step)
pm.summary(trace)
def test_summary_0d_variable_model():
mu = -2.1
tau = 1.3
with Model() as model:
x = Normal('x', mu, tau, testval=.1)
step = Metropolis(model.vars, np.diag([1.]), blocked=True)
trace = pm.sample(100, step=step)
pm.summary(trace)
def test_summary_1_value_model():
mu = -2.1
tau = 1.3
with Model() as model:
x = Normal('x', mu, tau, testval=.1)
step = Metropolis(model.vars, np.diag([1.]))
trace = sample(100, step=step)
pm.summary(trace)
def test_summary_2d_variable_model():
mu = -2.1
tau = 1.3
with Model() as model:
x = Normal('x', mu, tau, shape=(2, 2),
testval=np.tile(.1, (2, 2)))
step = Metropolis(model.vars, np.diag([1.]))
trace = sample(100, step=step)
pm.summary(trace)
def test_summary_2dim_value_model():
mu = -2.1
tau = 1.3
with Model() as model:
x = Normal('x', mu, tau, shape=(2, 2), testval=np.tile(.1, (2, 2)))
step = Metropolis(model.vars, np.diag([1.]))
trace = sample(100, step=step)
with warnings.catch_warnings(record=True) as wrn:
pm.summary(trace)
assert len(wrn) == 1
assert str(wrn[0].message) == 'Skipping x (above 1 dimension)'
def test_summary_2dim_value_model():
mu = -2.1
tau = 1.3
with Model() as model:
x = Normal('x', mu, tau, shape=(2, 2),
testval=np.tile(.1, (2, 2)))
step = Metropolis(model.vars, np.diag([1.]))
trace = sample(100, step=step)
with warnings.catch_warnings(record=True) as wrn:
pm.summary(trace)
assert len(wrn) == 1
assert str(wrn[0].message) == 'Skipping x (above 1 dimension)'