A Nonstationary Designer Space-Time Kernel
For spatial statisticians modeling time-evolving phenomena, this provides a more natural kernel design, though it is an incremental methodological contribution.
The paper proposes a new nonstationary kernel for spatial statistics that is defined over the half-line to better model time-dependent phenomena with asymmetry, addressing limitations of stationary covariance structures.
In spatial statistics, kriging models are often designed using a stationary covariance structure; this translation-invariance produces models which have numerous favorable properties. This assumption can be limiting, though, in circumstances where the dynamics of the model have a fundamental asymmetry, such as in modeling phenomena that evolve over time from a fixed initial profile. We propose a new nonstationary kernel which is only defined over the half-line to incorporate time more naturally in the modeling process.