Example of the forced sorted priors from polychord.

forced_sorted_priors.py

import numpy as np


# From pypolychord/priors.py
class UniformPrior:
    def __init__(self, a, b):
        self.a = a
        self.b = b

    def __call__(self, x):
        return self.a + (self.b-self.a) * x


def forced_indentifiability_transform(x):
    N = len(x)
    t = np.zeros(N)
    t[N-1] = x[N-1]**(1./N)
    for n in range(N-2, -1, -1):
        t[n] = x[n]**(1./(n+1)) * t[n+1]
    return t


class SortedUniformPrior(UniformPrior):
    def __call__(self, x):
        t = forced_indentifiability_transform(x)
        return super(SortedUniformPrior, self).__call__(t)


def prior(hypercube):
    """ Uniform prior from [-10,10]^D. """
    return SortedUniformPrior(-10, 10)(hypercube)


# Polychord generate in unit cude
ndim = 5
hyper_points = np.atleast_2d([np.random.uniform(0, 1, ndim) for i in range(10000)])

# This corresponds to physical space
phys_points = np.atleast_2d([prior(hyper_point) for hyper_point in hyper_points])


import matplotlib.pyplot as plt
fig, axes = plt.subplots(1, 1)
for dim in range(ndim):
    axes.hist(hyper_points[:, dim], alpha=0.2, label="dim = {}".format(dim),
              density=True)
axes.legend()
axes.set_title("HyperCube space")
fig.show()


import matplotlib.pyplot as plt
fig, axes = plt.subplots(1, 1)
for dim in range(ndim):
    axes.hist(phys_points[:, dim], alpha=0.2, label="dim = {}".format(dim),
              density=True)
axes.legend()
axes.set_title("Phys space")
fig.show()