def test_glm_from_formula(self):
with Model() as model:
NAME = 'glm'
GLM.from_formula('y ~ x', self.data_linear, name=NAME)
start = find_MAP()
step = Slice(model.vars)
trace = sample(500, step=step, start=start, progressbar=False, random_seed=self.random_seed)
assert round(abs(np.mean(trace['%s_Intercept' % NAME])-self.intercept), 1) == 0
assert round(abs(np.mean(trace['%s_x' % NAME])-self.slope), 1) == 0
assert round(abs(np.mean(trace['%s_sd' % NAME])-self.sd), 1) == 0
def test_glm_from_formula(self):
with Model() as model:
NAME = 'glm'
GLM.from_formula('y ~ x', self.data_linear, name=NAME)
start = find_MAP()
step = Slice(model.vars)
trace = sample(500, step=step, start=start, progressbar=False, random_seed=self.random_seed)
self.assertAlmostEqual(np.mean(trace['%s_Intercept' % NAME]), self.intercept, 1)
self.assertAlmostEqual(np.mean(trace['%s_x' % NAME]), self.slope, 1)
self.assertAlmostEqual(np.mean(trace['%s_sd' % NAME]), self.sd, 1)
def test_glm_from_formula(self):
with Model() as model:
NAME = "glm"
GLM.from_formula("y ~ x", self.data_linear, name=NAME)
start = find_MAP()
step = Slice(model.vars)
trace = sample(
500, tune=0, step=step, start=start, progressbar=False, random_seed=self.random_seed
)
assert round(abs(np.mean(trace["%s_Intercept" % NAME]) - self.intercept), 1) == 0
assert round(abs(np.mean(trace["%s_x" % NAME]) - self.slope), 1) == 0
assert round(abs(np.mean(trace["%s_sd" % NAME]) - self.sigma), 1) == 0
def pooled_model(X,y):
'''
This function build a pooled model in PyMC3. This function will only work
with four independent variables in the X matrix.
INPUT: X - an np array containing a standardized variable matrix
with four variables
y - an np array containing the target values
OUTPUT: pooled_model - a PyMC3 model object
trace - a PyMC3 trace object
'''
data = dict(x1=X[:,0], x2=X[:,1], x3=X[:,2], x4=X[:,3], y=y)
with Model() as pooled_model:
# specify glm and pass in data. The resulting linear model, its likelihood and
# and all its parameters are automatically added to our model.
GLM.from_formula('y ~ 1 + x1 + x2 + x3 +x4', data)
# draw 3000 posterior samples using NUTS sampling
trace = sample(1000, n_init=50000, tune=1000, njobs=1)
return pooled_model, trace
def unpooled_model(X, y, level, n_levels):
'''
This function build a unpooled model in PyMC3. This function will only work
with four independent variables in the X matrix.
INPUT: X - an np array containing a standardized variable matrix
with four variables
y - an np array containing the target values
level - an array with the level value for each row of the matrix
n_levels - an INT indicating the number of unique level names
OUTPUT: unpooled_model - a PyMC3 model object
unpooled_trace - a PyMC3 trace object
'''
with Model() as unpooled_model:
intercept = Normal('intercept', 0, sd=1e5, shape=n_levels)
beta1 = Normal('beta1', 0, sd=1e5)
beta2 = Normal('beta2', 0, sd=1e5)
beta3 = Normal('beta3', 0, sd=1e5)
beta4 = Normal('beta4', 0, sd=1e5)
sigma = HalfCauchy('sigma', 5)
theta = intercept[level] + beta1 * X[:,0] + beta2 * X[:,1] + beta3 * X[:,2] + beta4 * X[:,3]
y = Normal('y', theta, sd=sigma, observed=y)
with unpooled_model:
unpooled_trace = sample(1000, n_init=50000, tune=1000)
return unpooled_model, unpooled_trace
def multi_model(X, y, level, n_levels):
'''
This function build a unpooled model in PyMC3. This function will only work
with four independent variables in the X matrix.
INPUT: X - an np array containing a standardized variable matrix
with four variables
y - an np array containing the target values
level - an array with the level value for each row of the matrix
n_levels - an INT indicating the number of unique level names
OUTPUT: multi_model - a PyMC3 model object
multi_trace - a PyMC3 trace object
'''
with Model() as multi_model:
#set intercept hyper priors
mu_intercept = Normal('mu_intercep', mu=0., sd=1e5)
sigma_intercept = HalfCauchy('sigma_intercep', 5)
#set beta1 hyper priors
mu_beta1 = Normal('mu_beta1', mu=0., sd=1e5)
sigma_beta1 = HalfCauchy('sigma_beta1', 5)
#set beta2 hyper priors
mu_beta2 = Normal('mu_beta2', mu=0., sd=1e5)
sigma_beta2 = HalfCauchy('sigma_beta2', 5)
#set beta3 hyper priors
mu_beta3 = Normal('mu_beta3', mu=0., sd=1e5)
sigma_beta3 = HalfCauchy('sigma_beta3', 5)
#set beta4 hyper priors
mu_beta4 = Normal('mu_beta4', mu=0., sd=1e5)
sigma_beta4 = HalfCauchy('sigma_beta4', 5)
intercept = Normal('intercept', mu=mu_intercept, sd=sigma_intercept, shape=n_levels)
beta1 = Normal('beta1', mu=mu_beta1, sd=sigma_beta1, shape=n_levels)
beta2 = Normal('beta2', mu=mu_beta2, sd=sigma_beta2, shape=n_levels)
beta3 = Normal('beta3', mu=mu_beta3, sd=sigma_beta3, shape=n_levels)
beta4 = Normal('beta4', mu=mu_beta3, sd=sigma_beta4, shape=n_levels)
sigma = HalfCauchy('sigma', 5)
HIV_like = intercept[level] + beta1[level] * X[:,0] + beta2[level] * X[:,1] + beta3[level] * X[:,2] + beta4[level] * X[:,3]
y = Normal('y', HIV_like, sd=sigma, observed=y)
with multi_model:
multi_trace = sample(1000, n_init=150000, tune=50000)
return multi_model, multi_trace
def score_model(model, trace):
waic_score = stats.waic(model=model, trace=trace)
loo_score = stats.loo(model=pooled_model_X, trace=pooled_X_trace)
print('WAIC for this model is {} ({})'.format(round(waic_score[0], 2),
round(waic_score[1], 2)))
print('LOO for this model is {} ({})'.format(round(loo_score[0], 2),
round(loo_score[1], 2)))
if __name__ == '__main__':
df = load.load_all_data(2015)
df_no_zero_outlier = df[((df.HIVincidence > 0) & (df.HIVincidence < 130))].copy()
us_states, n_states, state = make_levels(df_no_zero_outlier, 'STATEABBREVIATION')
print(us_states, n_states, state)
#ax3.set_ylabel("")
ax1.set_xticklabels(['Ketamine', 'Midazolam'], fontsize=14)
ax2.set_xticklabels(['Ketamine', 'Midazolam'], fontsize=14)
#ax3.set_xticklabels(['Ketamine', 'Midazolam'], fontsize=14)
fig.savefig("changeCorrelation.png", dpi=300, bbox_inches='tight')
# %% [markdown]
# ## Use PyMC3 to compare the difference in correlation
# %%
# Using Pymc3
import pymc3 as pm
from pymc3.glm import GLM
with pm.Model() as model_glm:
GLM.from_formula('amg_hipp_change ~ groupIdx', dfCors)
trace = pm.sample(draws=4000, tune=3000)
# %%
pm.summary(trace, credible_interval=.95).round(2)
# %%
# Using Pymc3 - compare antrior hippo and antvmpfc
with pm.Model() as model_glm2:
GLM.from_formula('hippoAnt_vmpfcAnt_change ~ groupIdx', dfCors)
trace2 = pm.sample(draws=4000, tune=2000)
# %%
pm.summary(trace2, credible_interval=.95).round(2)
# %%
from pymc3.glm import GLM
import pylab as plt
import pandas
from scipy.stats import uniform, norm
# Data
np.random.seed(1056) # set seed to replicate example
nobs= 250 # number of obs in model
x1 = uniform.rvs(size=nobs) # random uniform variable
beta0 = 2.0 # intercept
beta1 = 3.0 # angular coefficient
xb = beta0 + beta1 * x1 # linear predictor, xb
y = norm.rvs(loc=xb, scale=1.0, size=nobs) # create y as adjusted
# Fit
df = pandas.DataFrame({'x1': x1, 'y': y}) # re-write data
with Model() as model_glm:
GLM.from_formula('y ~ x1', df)
trace = sample(5000)
# Output
summary(trace)
# show graphical output
traceplot(trace)
plt.show()
def get_mcmc_betas(train_Ys, train_Xs):
"""
:return mcmc_betas: (Series) Coefficients of intercept and betas.
"""
print('train_size:', len(train_Xs))
train_data = pandas.DataFrame({
'Y': train_Ys,
'X_1': train_Xs[:, 1],
'X_2': train_Xs[:, 2],
'X_3': train_Xs[:, 3],
'X_4': train_Xs[:, 4],
'X_5': train_Xs[:, 5],
'X_6': train_Xs[:, 6],
'X_7': train_Xs[:, 7],
'X_8': train_Xs[:, 8],
'X_9': train_Xs[:, 9],
'X_10': train_Xs[:, 10],
'X_11': train_Xs[:, 11],
'X_12': train_Xs[:, 12],
'X_13': train_Xs[:, 13],
'X_14': train_Xs[:, 14],
'X_15': train_Xs[:, 15],
'X_16': train_Xs[:, 16],
'X_17': train_Xs[:, 17],
'X_18': train_Xs[:, 18],
'X_19': train_Xs[:, 19],
'X_20': train_Xs[:, 20],
'X_21': train_Xs[:, 21],
'X_22': train_Xs[:, 22],
'X_23': train_Xs[:, 23],
'X_24': train_Xs[:, 24],
'X_25': train_Xs[:, 25],
'X_26': train_Xs[:, 26],
'X_27': train_Xs[:, 27],
'X_28': train_Xs[:, 28],
'X_29': train_Xs[:, 29],
'X_30': train_Xs[:, 30],
'X_31': train_Xs[:, 31],
'X_32': train_Xs[:, 32],
'X_33': train_Xs[:, 33],
'X_34': train_Xs[:, 34],
'X_35': train_Xs[:, 35],
'X_36': train_Xs[:, 36],
'X_37': train_Xs[:, 37],
'X_38': train_Xs[:, 38],
'X_39': train_Xs[:, 39],
'X_40': train_Xs[:, 40],
'X_41': train_Xs[:, 41],
'X_42': train_Xs[:, 42],
'X_43': train_Xs[:, 43],
'X_44': train_Xs[:, 44],
'X_45': train_Xs[:, 45]
})
with pm.Model():
GLM.from_formula(
'Y ~ X_1 + X_2 + X_3 + X_4 + X_5 + X_6 + X_7 + X_8 + X_9 + X_10'
' + X_11 + X_12 + X_13 + X_14 + X_15 + X_16 + X_17 + X_18 + X_19 + X_20'
' + X_21 + X_22 + X_23 + X_24 + X_25 + X_26 + X_27 + X_28 + X_29 + X_30'
' + X_31 + X_32 + X_33 + X_34 + X_35 + X_36 + X_37 + X_38 + X_39 + X_40'
' + X_41 + X_42 + X_43 + X_44 + X_45',
train_data,
family=Binomial())
trace = pm.sample(cores=os.cpu_count())
summary = pm.summary(trace)
pm.traceplot(trace)
plt.savefig('stats/posterior_distribution.png')
plt.show()
mcmc_betas = summary['mean']
return mcmc_betas