Journal
INVERSE PROBLEMS
Volume 36, Issue 5, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1361-6420/ab762e
Keywords
inverse problems; variogram; Bayesian methods; boundary conditions; Whittle-Matern; stochastic partial differential equations; Gaussian field
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Funding
- Gordon Preston Fellowship
- Australian Research Council [CE140100049]
- Australian Research Council [CE140100049] Funding Source: Australian Research Council
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We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance operators defined by the Matern covariance function and Gaussian processes with precision (inverse-covariance) operators defined by the Green's functions of a class of elliptic stochastic partial differential equations (SPDEs). We present a detailed mathematical description of this connection. We will show that there is an equivalence between these two Gaussian processes when the domain is infinite-for us, R2
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