paramonte.vis.kde2d
¶
Module Contents¶
Functions¶

Return the 2d density map from discrete observations via 

paramonte.vis.kde2d.
kde2d
(x, y, n=256, limits=None)[source]¶ Return the 2d density map from discrete observations via 2dimensional diffusion Kernel density estimation.
First the input data is binned. After binning, the function determines the optimal bandwidth according to the diffusionbased method. It then smooths the binned data over the grid using a Gaussian kernel with a standard deviation corresponding to that bandwidth.
This module is based on the KDE estimation method of
Z. I. Botev, J. F. Grotowski, D. P. Kroese: Kernel density estimation via diffusion. Annals of Statistics 38 (2010), no. 5, 2916–2957. doi:10.1214/10AOS799
and
John Hennig DOI: 10.5281/zenodo.3830437
Parameters
x
A lists of array of numbers that represent discrete observations of a random variable with two coordinate components. The observations are binned on a grid of n*n points, where
n
must be a power of 2 or will be coerced to the next one. Ifx
andy
are not the same length, the algorithm will raise aValueError
.y
A lists of array of numbers that represent discrete observations of a random variable with two coordinate components. The observations are binned on a grid of n*n points, where
n
must be a power of 2 or will be coerced to the next one. Ifx
andy
are not the same length, the algorithm will raise aValueError
.n (optional)
The number of grid points. It must be a power of 2. Otherwise, it will be coerced to the next power of two. The default is 256.
limits (optional)
Data
limits
specified as a tuple of tuples denoting((xmin, xmax), (ymin, ymax))
. If any of the values areNone
, they will be inferred from the data. Each tuple, or even both of them, may also be replaced by a single value denoting the upper bound of a range centered at zero. The default isNone
.Returns
A tuple whose elements are the following:
density
The density map of the data.
grid
The grid at which the density is computed.
bandwidth
The optimal values (per axis) that the algorithm has determined. If the algorithm does not converge, it will raise a
ValueError
.