def __init__(self,
name,
parent,
samples,
alpha,
pi,
freezer,
logspace=False):
Interval.__init__(self, samples, alpha, ndim=1)
self.name = name
self.parent = parent
# method for computing p(theta | data)
self.pi = pi
self.freezer = freezer
# compute the hpd interval
# Adapted from "Monte Carlo Estimation of Bayesian Credible and HPD Intervals", Ming-Hui Chen and Qi-Man Shao, 1999
# self.epsilon = [self.pi(t) for t in self.samples]
self.epsilon = [self.compute_pi(sample=t) for t in self.samples]
self.epsilon.sort()
j = int(self.n * self.alpha)
self.epj = self.epsilon[
j] # any observation with pi(x|D) > epj is in the region
self.paramSamples = [s[parent][name] for s in self.samples]
self.paramSamples.sort()
self.lb = self.paramSamples[int(self.n * self.alpha)]
self.ub = self.paramSamples[int(self.n * (1 - self.alpha))]
def __init__(self, samples, alpha, start=1e-6, tol=1e-6, maxiter=100):
Interval.__init__(self, samples, alpha, ndim=1)
p = samples.n
alphaPotential = 1. * np.arange(self.n) / self.n
self.alpha = filter(
lambda x: abs(x - self.alpha) == abs(self.alpha - alphaPotential).
min(), alphaPotential)[0]
self.mean = samples.array.mean(0)
self.std = samples.array.std(0)
self.lb, self.ub = self.mean - 2 * self.std, self.mean + 2 * self.std
self.epsilon = start
# function to calculate the empirical interval alpha for a given epsilon, x
check = lambda x: 1. * sum(
(self.samples.array > self.lb - x).all(1) &
(self.samples.array < self.ub + x).all(1)) / self.n
bounds = []
# double to find lower and upper epislon bound
while check(self.epsilon) < self.alpha:
bounds.append((self.epsilon, check(self.epsilon)))
self.epsilon *= 2
bounds.append((self.epsilon, check(self.epsilon)))
# binary search
eLb, eUb = self.epsilon / 2, self.epsilon
i = 0
while True:
if abs(check(eLb) - alpha) < tol:
self.epsilon = eLb
break
elif abs(check(eUb) - alpha) < tol:
self.epsilon = eUb
break
nb = (eLb + eUb) / 2
if check(nb) < alpha:
eLb = nb
bounds.append((nb, check(nb)))
else:
eUb = nb
bounds.append((nb, check(nb)))
i += 1
if i > maxiter:
self.epsilon = eLb
break
self.bounds = bounds
self.lb = self.mean - self.std - self.epsilon
self.ub = self.mean + self.std + self.epsilon
