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)
# EXAMINE THE RESULTS
burnin = 2000
thin = 1
# Print summary for each trace
zx = (x - x_m) / x_sd
zy = (y - y_m) / y_sd
tdf_gain = 100 # 1 for low-baised tdf, 100 for high-biased tdf
# THE MODEL
with pm.Model() as model:
# define the priors
beta0 = pm.Normal('beta0', mu=0, tau=1.0E-12)
beta1 = pm.Normal('beta1', mu=0, tau=1.0E-12)
tau = pm.Gamma('tau', 0.001, 0.001)
udf = pm.Uniform('udf', 0, 1)
tdf = 1 - tdf_gain * pm.log(1 - udf) # tdf in [1,Inf).
# define the likelihood
mu = beta0 + beta1 * zx
yl = pm.T('yl', mu=mu, lam=tau, nu=tdf, observed=zy)
# Generate a MCMC chain
start = pm.find_MAP()
step = [pm.Metropolis([rv]) for rv in model.unobserved_RVs]
trace = pm.sample(10000, step, start, progressbar=False)
# EXAMINE THE RESULTS
burnin = 1000
thin = 10
## Print summary for each trace
#pm.summary(trace[burnin::thin])
#pm.summary(trace)
## Check for mixing and autocorrelation
#pm.autocorrplot(trace[burnin::thin], vars =[tau])
NxLvl = len(set(x))
# # Construct list of all pairwise comparisons, to compare with NHST TukeyHSD:
contrast_dict = None
for g1idx in range(NxLvl):
for g2idx in range(g1idx + 1, NxLvl):
cmpVec = np.repeat(0, NxLvl)
cmpVec[g1idx] = -1
cmpVec[g2idx] = 1
contrast_dict = (contrast_dict, cmpVec)
z = (y - np.mean(y)) / np.std(y)
## THE MODEL.
with pm.Model() as model:
# define the hyperpriors
a_SD_unabs = pm.T('a_SD_unabs', mu=0, lam=0.001, nu=1)
a_SD = abs(a_SD_unabs) + 0.1
atau = 1 / a_SD**2
m = pm.Gamma('m', 1, 1)
d = pm.Gamma('d', 1, 1)
sG = m**2 / d**2
rG = m / d**2
# define the priors
sigma = pm.Uniform('sigma', 0,
10) # y values are assumed to be standardized
tau = pm.Gamma('tau', sG, rG)
a0 = pm.Normal('a0', mu=0,
tau=0.001) # y values are assumed to be standardized
a = pm.Normal('a', mu=0, tau=atau, shape=NxLvl)
mu = a0 + a
# define the likelihood
returns.plot(title='return of NIKKEI index close price', figsize=(30, 8))
nreturns = np.array(returns[1:])[::-1]
import pymc as pm
from pymc.distributions.timeseries import GaussianRandomWalk
from scipy.sparse import csc_matrix
from scipy import optimize
with pm.Model() as model:
sigma, log_sigma = model.TransformedVar(
'sigma', pm.Exponential.dist(1. / .02, testval=.1), pm.logtransform)
nu = pm.Exponential('nu', 1. / 10)
s = GaussianRandomWalk('s', sigma**-2, shape=len(nreturns))
r = pm.T('r', nu, lam=pm.exp(-2 * s), observed=nreturns)
with model:
start = pm.find_MAP(vars=[s], fmin=optimize.fmin_l_bfgs_b)
step = pm.NUTS(scaling=start)
trace = pm.sample(2000, step, start, progressbar=False)
plt.plot(trace[s][::10].T, 'b', alpha=.03)
plt.title('log volatility')
with model:
pm.traceplot(trace, model.vars[:2])
exps = np.exp(trace[s][::10].T)
plt.plot(returns[:600][::-1])
plt.plot(exps, 'r', alpha=.03)