Matérn kernel regression (2): 2nd 3rd and fractional order, splines, Gaussian filter examples

Antonio Sala, UPV

Difficulty: ***** ,       Relevance: ,      Duration: 17:25

Summary:

This video, a continuation of [maternr1EN], discusses the Matérn cases of spectral factor of order 2 and 3. When the correlation distance $\rho$ increases, the interpolated mean tends to be a cubic spline (in case of order 2 spectral factor) and a quintic spline (in case of order 3), respectively.

The final part of the video presents an example of fractional order ($n=1.5$) of the spectral factor (this motivates definitions of ’fractional derivatives’ in literature, which are not the subject of this material), and an example with a quadratic exponential kernel, which is the Matérn limit when the order of the spectral factor tends to infinity (whose interpolation would be infinitely differentiable), as discussed in video [maternEN].

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.