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import numpy as np
from scipy.stats import multivariate_normal as mvn
import kombine
Import some cool visualization stuff.
In [2]:
from matplotlib import pyplot as plt
import corner
import prism
%matplotlib inline
%config InlineBackend.figure_format = 'retina'
prism.inline_ipynb()
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ndim = 2
Construct a pickleable, callable object to hold the target distribution.
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class Target(object):
def __init__(self, cov):
self.cov = cov
self.ndim = self.cov.shape[0]
def logpdf(self, x):
return mvn.logpdf(x, mean=np.zeros(self.ndim), cov=self.cov)
def __call__(self, x):
return self.logpdf(x)
Generate a random covariance matrix and construct the target.
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A = np.random.rand(ndim, ndim)
cov = A*A.T + ndim*np.eye(ndim);
lnpdf = Target(cov)
Create a uniformly distributed ensemble and burn it in.
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nwalkers = 500
sampler = kombine.Sampler(nwalkers, ndim, lnpdf)
p0 = np.random.uniform(-10, 10, size=(nwalkers, ndim))
p, post, q = sampler.burnin(p0)
See what burnin did.
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prism.corner(sampler.chain)
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Generate some more samples.
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p, post, q = sampler.run_mcmc(100)
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fig, [ax1, ax2, ax3] = plt.subplots(1, 3, figsize=(15, 5))
ax1.plot(sampler.acceptance_fraction, 'k', alpha=.5, label="Mean Acceptance Rate");
for p, ax in zip(range(sampler.dim), [ax2, ax3]):
ax.plot(sampler.chain[..., p], alpha=0.1)
ax1.legend(loc='lower right');
Plot independent samples.
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acls = np.ceil(2/np.mean(sampler.acceptance[-100:], axis=0) - 1).astype(int)
ind_samps = np.concatenate([sampler.chain[-100::acl, c].reshape(-1, 2) for c, acl in enumerate(acls)])
print("{} independent samples collected with a mean ACL of {}.".format(len(ind_samps), np.mean(acls)))
corner.corner(ind_samps);
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