Spatial variation : Stochastic models and their application to some problems in forest surveys and other sampling investigations

By B. Matérn. 1960

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, methodology): “Like the Matérn processes, RSA is a hard-core model, designed primarily to capture packing distributions, with much of the theoretical analysis focused on the achievable density.”
Robots that can adapt like animals (2014, methodology): “The Matérn kernel function is computed as follows 43,44 (with ν = 5 / 2 ): ); and (viii) A random selection without replacement from subcomponents of all the available behavior descriptors (i-vii) ( Random ).”
IS QUASAR OPTICAL VARIABILITY A DAMPED RANDOM WALK? (2012, unknown): “The “Matérn” (MA) covariance function (Matérn 1960) is defined by SMA(∆t) = σ 2 2 1−ν Γ(ν) (√ 2ν|∆t| τ )ν Kν (√ 2ν∆t τ ) with ν > 0 (6) where Γ is the gamma function, Kν is a modified Bessel function of the second kind, and the new parameter, ν primarily adjusts the correlation function on short…”
Decoupling the Short- and Long-Term Behavior of Stochastic Volatility (2016, background): “We note that cX is the Matérn covariance function (Matérn, 1960; Handcock and Stein, 1993), which is widely used in many areas of statistics, e.g., spatial statistics, geostatistics, and machine learning.”
Random Fields and Geometry (2007, result): “For example, we have the following result, due to Matérn [104].”
Some new random field tools for spatial analysis (2008, background): “Perhaps the first studied example of a real valued random field in two dimensions is due to Matérn [10], who modelled forestry yields f (x) as a function of a twodimensional positional variable x.”
Estimating and modeling space–time correlation structures (2001, background): “That is, for any (si, ti) ∈ D×T , any ai ∈ , i = 1, . . . , n, and any positive integer n, Cst must satisfy: n∑ i=1 n∑ j=1 aiajCst(si − sj, ti − tj) ≥ 0 For continuous functions, positive-definiteness is equivalent to the process having a spectral distribution function (Matern, 1960).”
Kalman filtering and smoothing solutions to temporal Gaussian process regression models (2010, methodology): “In this article we aim to represent the random process f(t) having the covariance function k(τ) as output of a linear time invariant (LTI) stochastic differential equation (SDE), which are efficient to analyse with Kalman filtering theory discussed in Section 5.”
Spatio-temporal variograms and covariance models (2005, background): “Some properties of the von Kármán–Whittle model, which is often named the Matérn model in the statistical literature, were demonstrated in Matérn (1986), Kent (1989), and Stein (1999).”
The debiased Whittle likelihood (2019, methodology): “The Matérn process In this section we investigate the performance of the debiased Whittle likelihood in a Monte Carlo study using observations from a Matérn process (Matérn, 1960), as motivated by the simulation studies ofAnitescu et al. (2012), who investigated the same process.”
Perfect simulation and moment properties for the Matérn type III process (2010, background): “it is harder to simulate from Matérn III than from Matérn I or II, it is still feasible to make perfect simulations and hence to study the properties of Matérn III experimentally. Section 4 provides Monte Carlo estimates of the packing density of Matérn III, which can be much higher than for Matérn ”