Gaussian Process Modeling of Derivative Curves

Relative sea-level change in Connecticut (USA) during the last 2200 yrs

“…We model the rate of sea-level change (i.e. the first derivative) and 220 subsequently integrate it to form an integrated Gaussian process (IGP; Holsclaw et al, 2013), which aims 221 to match RSL. The Gaussian process has a prior distribution specified by a mean function (here set to a 222 constant) and a covariance function that determines the smoothness of the reconstructions.…”

Approximate Bayesian inference in semi-mechanistic models

“…(1) in Holsclaw et al (2013). This acts as a proxy for the missing rates y i (t) on the left-hand side of Eq.…”

“…In the present work, we apply a GP to smooth interpolation and exploit the fact that GPs are closed under differentiation, i.e. provided the kernel is differentiable, the derivative of a GP is also a GP, and its covariance matrix can be derived (Solak et al 2002;Holsclaw et al 2013). 1 We provide more details in the following section.…”

“…Finally, we took the first derivative of each of the implemented kernel functions, replaced the original covariance matrix with the one derived from the derivative functions, and then applied Eq. (1) in Holsclaw et al (2013) to obtain the expectation of the derivative for each time point.…”

Kriging-based estimation of time derivatives via FIR filtering

“…Methods for evaluating derivatives based on Kriging have been proposed in [11,12]. The method advocated in this paper elaborates from these previous works to propose a practical scheme for estimating successive time derivatives at a low computational cost, under the form of a finite impulse response (FIR) filter with constant coefficients, in the case of regularly spaced samples.…”