Weighted Gaussian kernel density estimation in `python`
Update: Weighted samples are now supported by scipy.stats.gaussian_kde. See here and here for details.
It is currently not possible to use scipy.stats.gaussian_kde to estimate the density of a random variable based on weighted samples. What methods are available to estimate densities of continuous random variables based on weighted samples?
Answer
Neither sklearn.neighbors.KernelDensity nor statsmodels.nonparametric seem to support weighted samples. I modified scipy.stats.gaussian_kde to allow for heterogeneous sampling weights and thought the results might be useful for others. An example is shown below.
An ipython notebook can be found here: http://nbviewer.ipython.org/gist/tillahoffmann/f844bce2ec264c1c8cb5
Implementation details
The weighted arithmetic mean is
The unbiased data covariance matrix is then given by
The bandwidth can be chosen by scott or silverman rules as in scipy. However, the number of samples used to calculate the bandwidth is Kish's approximation for the effective sample size.