Getting bandwidth used by SciPy's gaussian_kde function

Question

I'm using SciPy's stats.gaussian_kde function to generate a kernel density estimate (kde) function from a data set of x,y points.

This is a simple MWE of my code:

import numpy as np
from scipy import stats

def random_data(N):
    # Generate some random data.
    return np.random.uniform(0., 10., N)

# Data lists.
x_data = random_data(100)
y_data = random_data(100)

# Obtain the gaussian kernel.
kernel = stats.gaussian_kde(np.vstack([x_data, y_data]))

Since I'm not setting a bandwidth manually (via the bw_method key), the function defaults to using Scott's rule (see function's description). What I need is to obtain this bandwidth value set automatically by the stats.gaussian_kde function.

I've tried using:

print kernel.set_bandwidth()

but it always returns None instead of a float.

Answer 1

Short answer

The bandwidth is kernel.covariance_factor() multiplied by the std of the sample that you are using.

(This is in the case of 1D sample and it is computed using Scott's rule of thumb in the default case).

Example:

from scipy.stats import gaussian_kde
sample = np.random.normal(0., 2., 100)
kde = gaussian_kde(sample)
f = kde.covariance_factor()
bw = f * sample.std()

The pdf that you get is this:

from pylab import plot
x_grid = np.linspace(-6, 6, 200)
plot(x_grid, kde.evaluate(x_grid))

You can check it this way, If you use a new function to create a kde using, say, sklearn:

from sklearn.neighbors import KernelDensity
def kde_sklearn(x, x_grid, bandwidth):
    kde_skl = KernelDensity(bandwidth=bandwidth)
    kde_skl.fit(x[:, np.newaxis])
    # score_samples() returns the log-likelihood of the samples
    log_pdf = kde_skl.score_samples(x_grid[:, np.newaxis])
    pdf = np.exp(log_pdf)
    return pdf

Now using the same code from above you get:

plot(x_grid, kde_sklearn(sample, x_grid, f))

plot(x_grid, kde_sklearn(sample, x_grid, bw))