# Kernel Density Estimation (ligo.skymap.kde)¶

class ligo.skymap.kde.BoundedKDE(pts, low=- inf, high=inf, periodic=False, bw_method=None)[source] [edit on github]

Density estimation using a KDE on bounded domains.

Bounds can be any combination of low or high (if no bound, set to float('inf') or float('-inf')), and can be periodic or non-periodic. Cannot handle topologies that have multi-dimensional periodicities; will only handle topologies that are direct products of (arbitrary numbers of) R, [0,1], and S1.

Parameters
ptsnumpy.ndarray

(Ndim, Npts) shaped array of points (as in gaussian_kde).

low

Lower bounds; if None, assume no lower bounds.

high

Upper bounds; if None, assume no upper bounds.

periodic

Boolean array giving periodicity in each dimension; if None assume no dimension is periodic.

bw_methodoptional

Bandwidth estimation method (see gaussian_kde).

evaluate(pts)[source] [edit on github]

Evaluate the KDE at the given points.

quantile(pt)[source] [edit on github]

Quantile of pt, evaluated by a greedy algorithm.

Parameters
pt

The point at which the quantile value is to be computed.

Notes

The quantile of pt is the fraction of points used to construct the KDE that have a lower KDE density than pt.

class ligo.skymap.kde.Clustered2DSkyKDE(pts, *args, **kwargs)[source] [edit on github]

Bases: ligo.skymap.kde.SkyKDE

Represents a kernel-density estimate of a sky-position PDF that has been decomposed into clusters, using a different kernel for each cluster.

The estimated PDF is

$p\left( \vec{\theta} \right) = \sum_{i = 0}^{k-1} \frac{N_i}{N} \sum_{\vec{x} \in C_i} N\left[\vec{x}, \Sigma_i\right]\left( \vec{\theta} \right)$

where $$C_i$$ is the set of points belonging to cluster $$i$$, $$N_i$$ is the number of points in this cluster, $$\Sigma_i$$ is the optimally-converging KDE covariance associated to cluster $$i$$.

The number of clusters, $$k$$ is chosen to maximize the BIC for the given set of points being drawn from the clustered KDE. The points are assigned to clusters using the k-means algorithm, with a decorrelated metric. The overall clustering behavior is similar to the well-known X-Means algorithm.

classmethod transform(pts)[source] [edit on github]

Override in sub-classes to transform points.

class ligo.skymap.kde.Clustered2Plus1DSkyKDE(pts, max_k=40, trials=5, assign=None, jobs=1)[source] [edit on github]

A hybrid sky map estimator that uses a 2D clustered KDE for the marginal distribution as a function of (RA, Dec) and a 3D clustered KDE for the conditional distance distribution.

posterior_spherical(pts)[source] [edit on github]

Evaluate the posterior probability density in spherical polar coordinates, as a function of (ra, dec, distance).

class ligo.skymap.kde.Clustered3DSkyKDE(pts, max_k=40, trials=5, assign=None, jobs=1)[source] [edit on github]

Bases: ligo.skymap.kde.SkyKDE

Like Clustered2DSkyKDE, but clusters in 3D space. Can compute volumetric posterior density (per cubic Mpc), and also produce Healpix maps of the mean and standard deviation of the log-distance.

as_healpix(top_nside=16)[source] [edit on github]

Return a HEALPix multi-order map of the posterior density and conditional distance distribution parameters.

posterior_spherical(pts)[source] [edit on github]

Evaluate the posterior probability density in spherical polar coordinates, as a function of (ra, dec, distance).

classmethod transform(pts)[source] [edit on github]

Override in sub-classes to transform points.