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from __future__ import division
import numpy as np
import scipy.stats.kde as kde
def calc_min_interval(x, alpha):
"""Internal method to determine the minimum interval of a given width
Assumes that x is sorted numpy array.
"""
n = len(x)
cred_mass = 1.0-alpha
interval_idx_inc = int(np.floor(cred_mass*n))
n_intervals = n - interval_idx_inc
interval_width = x[interval_idx_inc:] - x[:n_intervals]
if len(interval_width) == 0:
raise ValueError('Too few elements for interval calculation')
min_idx = np.argmin(interval_width)
hdi_min = x[min_idx]
hdi_max = x[min_idx+interval_idx_inc]
return hdi_min, hdi_max
def hdi(x, alpha=0.05):
"""Calculate highest posterior density (HPD) of array for given alpha.
The HPD is the minimum width Bayesian credible interval (BCI).
:Arguments:
x : Numpy array
An array containing MCMC samples
alpha : float
Desired probability of type I error (defaults to 0.05)
"""
# Make a copy of trace
x = x.copy()
# For multivariate node
if x.ndim > 1:
# Transpose first, then sort
tx = np.transpose(x, list(range(x.ndim))[1:]+[0])
dims = np.shape(tx)
# Container list for intervals
intervals = np.resize(0.0, dims[:-1]+(2,))
for index in make_indices(dims[:-1]):
try:
index = tuple(index)
except TypeError:
pass
# Sort trace
sx = np.sort(tx[index])
# Append to list
intervals[index] = calc_min_interval(sx, alpha)
# Transpose back before returning
return np.array(intervals)
else:
# Sort univariate node
sx = np.sort(x)
return np.array(calc_min_interval(sx, alpha))
def hdi2(sample, alpha=0.05, roundto=2):
"""Calculate highest posterior density (HPD) of array for given alpha.
The HPD is the minimum width Bayesian credible interval (BCI).
The function works for multimodal distributions, returning more than one mode
Parameters
----------
sample : Numpy array or python list
An array containing MCMC samples
alpha : float
Desired probability of type I error (defaults to 0.05)
roundto: integer
Number of digits after the decimal point for the results
Returns
----------
hpd: array with the lower
"""
sample = np.asarray(sample)
sample = sample[~np.isnan(sample)]
# get upper and lower bounds
l = np.min(sample)
u = np.max(sample)
density = kde.gaussian_kde(sample)
x = np.linspace(l, u, 2000)
y = density.evaluate(x)
#y = density.evaluate(x, l, u) waitting for PR to be accepted
xy_zipped = zip(x, y/np.sum(y))
xy = sorted(xy_zipped, key=lambda x: x[1], reverse=True)
xy_cum_sum = 0
hdv = []
for val in xy:
xy_cum_sum += val[1]
hdv.append(val[0])
if xy_cum_sum >= (1-alpha):
break
hdv.sort()
diff = (u-l)/20 # differences of 5%
hpd = []
hpd.append(round(min(hdv), roundto))
for i in range(1, len(hdv)):
if hdv[i]-hdv[i-1] >= diff:
hpd.append(round(hdv[i-1], roundto))
hpd.append(round(hdv[i], roundto))
hpd.append(round(max(hdv), roundto))
ite = iter(hpd)
hpd = list(zip(ite, ite))
modes = []
for value in hpd:
x_hpd = x[(x > value[0]) & (x < value[1])]
y_hpd = y[(x > value[0]) & (x < value[1])]
modes.append(round(x_hpd[np.argmax(y_hpd)], roundto))
return hpd, x, y, modes |