anesthetic.examples package

Module for generating example data of nested sampling.

anesthetic.examples.perfect_ns module

Perfect nested sampling generators.

anesthetic.examples.perfect_ns.correlated_gaussian(nlive, mean, cov, bounds=None, logLmax=0, *args, **kwargs)

Perfect nested sampling run for a correlated gaussian likelihood.

This produces a perfect nested sampling run with a uniform prior over the unit hypercube. The algorithm proceeds by simultaneously rejection sampling from the prior and sampling exactly and uniformly from the known ellipsoidal contours.

This can produce perfect runs in up to around d~15 dimensions. Beyond this rejection sampling from a truncated gaussian in the early stage becomes too inefficient.

Parameters:

nliveint

minimum number of live points across the run

mean1d array-like, shape (ndims,)

mean of gaussian in parameters. Length of array defines dimensionality of run.

cov2d array-like, shape (ndims, ndims)

covariance of gaussian in parameters

bounds2d array-like, shape (ndims, 2)

bounds of a gaussian, default [[0, 1]]*ndims

logLmaxfloat

maximum loglikelihood

The remaining arguments are passed to the

:class:`anesthetic.samples.NestedSamples` constructor.

Returns:

samplesanesthetic.samples.NestedSamples

Nested sampling run

anesthetic.examples.perfect_ns.gaussian(nlive, ndims, sigma=0.1, R=1, logLmin=-0.01, logLmax=0, *args, **kwargs)

Perfect nested sampling run for a spherical Gaussian & prior.

Up to normalisation this is identical to the example in John Skilling’s original paper https://doi.org/10.1214/06-BA127 . Both spherical Gaussian width sigma and spherical uniform prior width R are centered on zero

Parameters:

nliveint

number of live points

ndimsint

dimensionality of gaussian

sigmafloat

width of gaussian likelihood

Rfloat

radius of gaussian prior

logLminfloat

loglikelihood at which to terminate

logLmaxfloat

maximum loglikelihood

The remaining arguments are passed to the

:class:`anesthetic.samples.NestedSamples` constructor.

Returns:

samplesanesthetic.samples.NestedSamples

Nested sampling run

anesthetic.examples.perfect_ns.planck_gaussian(nlive=500)

Gaussian likelihood with Planck-like posterior.

This is a gaussian likelihood with the same mean, parameter covariance and average loglikelihood as the Planck 2018 legacy chains base/plikHM_TTTEEE_lowl_lowE_lensing

Parameters:

nliveint, optional

number of live points

Returns:

samplesanesthetic.samples.NestedSamples

Nested sampling run

anesthetic.examples.perfect_ns.wedding_cake(nlive, ndims, sigma=0.01, alpha=0.5, *args, **kwargs)

Perfect nested sampling run for a wedding cake likelihood.

This is a likelihood with nested hypercuboidal plateau regions of constant likelihood centered on 0.5, with geometrically decreasing volume by a factor of alpha. The value of the likelihood in these plateau regions has a gaussian profile with width sigma.

logL = - alpha^(2*floor(D*log_alpha(2|x-0.5|_infinity))/D) / (8sigma^2)

Parameters:

nliveint

number of live points

ndimsint

dimensionality of the likelihood

sigmafloat

width of gaussian profile

alphafloat

volume compression between plateau regions

The remaining arguments are passed to the

:class:`anesthetic.samples.NestedSamples` constructor.

anesthetic.examples.utils module

Utility functions for nested sampling examples.

anesthetic.examples.utils.log_volume_n_ball(n, r=1)

Log-volume of an n dimensional ball, radius r.

anesthetic.examples.utils.random_covariance(sigmas)

Draw a randomly oriented covariance matrix with axes length sigmas.

Parameters:

sigmas1d array like

Lengths of the axes of the ellipsoid.

Returns:

Covariance matrix2d np.array

shape (len(sigmas), len(sigmas)).

anesthetic.examples.utils.random_ellipsoid(mean, cov, size=None)

Draw a point uniformly in an ellipsoid.

This is defined so that the volume of the ellipsoid is sqrt(det(cov))*V_n. where V_n is the volume of the unit n ball, and so that its axes have length equal to the square root of the eigenvalues of the covariance matrix.

Parameters:

mean1d array-like

The center of mass of the ellipsoid

cov2d array-like

The covariance structure of the ellipsoid. Axes have lengths equal to the square root of the eigenvalues of this matrix.

sizeint or tuple of ints, optional

Given a shape of, for example, (m,n,k), m*n*k samples are generated, and packed in an m-by-n-by-k arrangement. Because each sample is N-dimensional, the output shape is (m,n,k,N). If no shape is specified, a single (N-D) sample is returned.

Returns:

pointsarray-like

The drawn samples, of shape size, if that was provided. If not, the shape is (N,). In other words, each entry out[i,j,...,:] is an N-dimensional value drawn uniformly from the ellipsoid.

anesthetic.examples.utils.volume_n_ball(n, r=1)

Volume of an n dimensional ball, radius r.