"Gaussian random field"의 두 판 사이의 차이

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* ID :  [https://www.wikidata.org/wiki/Q5527848 Q5527848]

2020년 12월 26일 (토) 05:15 판

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  1. A Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables.[1]
  2. The simplifications achieved by Gaussian random fields are based on fact that the joint Gaussian probability density function is fully determined by the mean and the covariance function.[2]
  3. Known results are extended from the finite‐dimensional case to the dimension‐free case; hence, in particular, to Gaussian random fields.[3]
  4. we recommend the package RandomFields (http://cran.r-project.org/src/contrib/PACKAGES.html#RandomFields) for a more comprehensive implementation for simulation of Gaussian Random Fields.[4]
  5. Clipped Gaussian random fields can be used for modeling discrete-valued random fields with a given correlation structure.[5]
  6. The computational complexity of realising an n × n lattice of points of a Gaussian random field in ℝ d depends considerably upon the structure of the covariance function.[6]
  7. On 𝕊 2 , similar results for isotropic Gaussian random fields also apply, i.e., we can perform a spectral decomposition into the spherical harmonic functions.[6]
  8. These can be sampled together with the derivatives point by point and then transformed to an isotropic Gaussian random field on the unit sphere by FFT.[6]
  9. In Section 2, we derive the decomposition of an isotropic Gaussian random field into 1d GMRFs via Fourier transforms, and compute the conditional covariance matrices.[6]
  10. We now review how probability distributions work for continuous, Gaussian random fields.[7]
  11. This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on ℝ2 based on dense observations of a single realization of the deformed random field.[8]
  12. VoI can be computed easily through updating a Gaussian random field, i.e., kriging, which is a probabilistic interpolation method.[9]

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