Covariance Function - Parametric Families of Covariance Functions

Parametric Families of Covariance Functions

A simple stationary parametric covariance function is the "exponential covariance function"

C(d) = \exp(-d/V)

where V is a scaling parameter, and d=d(x,y) is the distance between two points. Sample paths of a Gaussian process with the exponential covariance function are not smooth. The "squared exponential covariance function"

C(d) = \exp(-d^2/V)

is a stationary covariance function with smooth sample paths.

The Matérn covariance function and rational quadratic covariance function are two parametric families of stationary covariance functions. The Matérn family includes the exponential and squared exponential covariance functions as special cases.

Read more about this topic:  Covariance Function

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