I am trying to find if there exists a way to find the spatial distribution over a set of points where the points are weighted. If I have "n" points in the (x,y) space, I can fit a mixture of Gaussians to estimate a distribution. However, there might be situations where some points are more important than others so I have weights associated with my points. For example, the k-means algorithm can be extended to a weighted k-means problem. Is there a way to do so with a mixture of Gaussians?
SO has a post on this here but there are no accepted answers. I am having a similar problem and I thought this is a better forum.