When visualising one-dimensional data it's common to use the Kernel Density Estimation technique to account for improperly chosen bin widths.
When my one-dimensional dataset has measurement uncertainties, is there a standard way to incorporate this information?
For example (and forgive me if my understanding is naïve) KDE convolves a Gaussian profile with the delta functions of the observations. This Gaussian kernel is shared between each location, but the Gaussian $\sigma$ parameter could be varied to match the measurement uncertainties. Is there a standard way of performing this? I am hoping to reflect uncertain values with wide kernels.
I've implemented this simply in Python, but I do not know of a standard method or function to perform this. Are there any problems in this technique? I do note that it gives some strange looking graphs! For example
In this case the low values have larger uncertainties so tend to provide wide flat kernels, whereas the KDE over-weights the low (and uncertain) values.