Created
March 18, 2018 14:43
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from pymc import Normal, Uniform, MvNormal, Exponential | |
from numpy.linalg import inv, det | |
from numpy import log, pi, dot | |
import numpy as np | |
from scipy.special import gammaln | |
def _model(data, robust=False): | |
# priors might be adapted here to be less flat | |
mu = Normal('mu', 0, 0.000001, size=2) | |
sigma = Uniform('sigma', 0, 1000, size=2) | |
rho = Uniform('r', -1, 1) | |
# we have a further parameter (prior) for the robust case | |
if robust == True: | |
nu = Exponential('nu',1/29., 1) | |
# we model nu as an Exponential plus one | |
@pymc.deterministic | |
def nuplus(nu=nu): | |
return nu + 1 | |
@pymc.deterministic | |
def precision(sigma=sigma,rho=rho): | |
ss1 = float(sigma[0] * sigma[0]) | |
ss2 = float(sigma[1] * sigma[1]) | |
rss = float(rho * sigma[0] * sigma[1]) | |
return inv(np.mat([[ss1, rss], [rss, ss2]])) | |
if robust == True: | |
# log-likelihood of multivariate t-distribution | |
@pymc.stochastic(observed=True) | |
def mult_t(value=data.T, mu=mu, tau=precision, nu=nuplus): | |
k = float(tau.shape[0]) | |
res = 0 | |
for r in value: | |
delta = r - mu | |
enum1 = gammaln((nu+k)/2.) + 0.5 * log(det(tau)) | |
denom = (k/2.)*log(nu*pi) + gammaln(nu/2.) | |
enum2 = (-(nu+k)/2.) * log (1 + (1/nu)*delta.dot(tau).dot(delta.T)) | |
result = enum1 + enum2 - denom | |
res += result[0] | |
return res[0,0] | |
else: | |
mult_n = MvNormal('mult_n', mu=mu, tau=precision, value=data.T, observed=True) | |
return locals() | |
def analyze(data, robust=False, plot=True): | |
model = pymc.MCMC(_model(data,robust)) | |
model.sample(50000,25000) | |
if plot: | |
pymc.Matplot.plot(model) | |
return model |
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