# Random Y values generated from linear model with true parameter values:
y = np.sum(x * beta_true[1:].T, axis=1) + beta_true[0] + norm.rvs(0, sd_true, n_data)
# Select which predictors to include
include_only = list(range(0, n_predictors)) # default is to include all
#x = x.iloc[include_only]
predictor_names = x.columns
n_predictors = len(predictor_names)
# THE MODEL
with pm.Model() as model:
# define hyperpriors
muB = pm.Normal('muB', 0,.100 )
tauB = pm.Gamma('tauB', .01, .01)
udfB = pm.Uniform('udfB', 0, 1)
tdfB = 1 + tdfBgain * (-pm.log(1 - udfB))
# define the priors
tau = pm.Gamma('tau', 0.01, 0.01)
beta0 = pm.Normal('beta0', mu=0, tau=1.0E-12)
beta1 = pm.T('beta1', mu=muB, lam=tauB, nu=tdfB, shape=n_predictors)
mu = beta0 + pm.dot(beta1, x.values.T)
# define the likelihood
#mu = beta0 + beta1[0] * x.values[:,0] + beta1[1] * x.values[:,1]
yl = pm.Normal('yl', mu=mu, tau=tau, observed=y)
# Generate a MCMC chain
start = pm.find_MAP()
step1 = pm.NUTS([beta1])
step2 = pm.Metropolis([beta0, tau, muB, tauB, udfB])
trace = pm.sample(10000, [step1, step2], start, progressbar=False)
# Re-center data at mean, to reduce autocorrelation in MCMC sampling.
# Standardize (divide by SD) to make initialization easier.
x_m = np.mean(x)
x_sd = np.std(x)
y_m = np.mean(y)
y_sd = np.std(y)
zx = (x - x_m) / x_sd
zy = (y - y_m) / y_sd
tdf_gain = 1 # 1 for low-baised tdf, 100 for high-biased tdf
# THE MODEL
with pm.Model() as model:
# define the priors
udf = pm.Uniform('udf', 0, 1)
tdf = 1 - tdf_gain * pm.log(1 - udf) # tdf in [1,Inf).
tau = pm.Gamma('tau', 0.001, 0.001)
beta0 = pm.Normal('beta0', mu=0, tau=1.0E-12)
beta1 = pm.Normal('beta1', mu=0, tau=1.0E-12)
mu = beta0 + beta1 * zx
# define the likelihood
yl = pm.T('yl', mu=mu, lam=tau, nu=tdf, observed=zy)
# Generate a MCMC chain
start = pm.find_MAP()
step = pm.Metropolis()
trace = pm.sample(20000, step, start, progressbar=False)
# EXAMINE THE RESULTS
burnin = 1000
thin = 10
# Random Y values generated from linear model with true parameter values:
y = np.sum(x * beta_true[1:].T, axis=1) + beta_true[0] + norm.rvs(0, sd_true, n_data)
# Select which predictors to include
include_only = range(0, n_predictors) # default is to include all
#x = x.iloc[include_only]
predictor_names = x.columns
n_predictors = len(predictor_names)
# THE MODEL
with pm.Model() as model:
# define hyperpriors
muB = pm.Normal('muB', 0,.100 )
tauB = pm.Gamma('tauB', .01, .01)
udfB = pm.Uniform('udfB', 0, 1)
tdfB = 1 + tdfBgain * (-pm.log(1 - udfB))
# define the priors
tau = pm.Gamma('tau', 0.01, 0.01)
beta0 = pm.Normal('beta0', mu=0, tau=1.0E-12)
beta1 = pm.T('beta1', mu=muB, lam=tauB, nu=tdfB, shape=n_predictors)
mu = beta0 + pm.dot(beta1, x.values.T)
# define the likelihood
#mu = beta0 + beta1[0] * x.values[:,0] + beta1[1] * x.values[:,1]
yl = pm.Normal('yl', mu=mu, tau=tau, observed=y)
# Generate a MCMC chain
start = pm.find_MAP()
step1 = pm.NUTS([beta1])
step2 = pm.Metropolis([beta0, tau, muB, tauB, udfB])
trace = pm.sample(10000, [step1, step2], start, progressbar=False)
