simple kriging, ordinary kriging, universal kriging, and Bayesian kriging. In each case, there is a kriging predictor at every site, which depends on the data through a kriging vector. Combining the kriging predictor for all sites yields a kriging surface. The kriging variance describes the accuracy of the predictor at each site. Tables 7.1 and 7.2 set out the notation for kriging and Table 7.3 provides a comparison with some related notation used in machine learning.
The transfer covariance matrix and transfer drift matrix are used to construct the kriging predictor (Section 7.6).
Bordered covariance matrix. This is an matrix, Section 7.6.4, also used to construct the kriging predictor.
Autoregression (AR) and related spatial models come in various forms in Chapter 4 including:– MA: Moving average (Section 4.3)– SAR: Simultaneous autoregression (Section 4.5)– CAR: Conditional autoregression (Section 4.6)– ICAR: Intrinsic CAR (Section 4.6.3)– QICAR: Quasi‐intrinsic CAR (Section 4.6.3)– UAR: Unilateral autoregression (Section 4.8.2)– QAR: Quadrant unilateral autoregression (Section 4.8.3)
Types of matrix– Tensor product matrices (Section A.3.9)– Toeplitz, circulant, folded circulant matrices (Sections A.3.8 and A.10).– All circulant matrices in dimension have the same eigenvectors. These can be represented in complex coordinates by the unitary matrix or in real coordinates by the orthogonal matrix (Section A.7.2).
Abbreviations and terminology for estimation and testing:– MLE: maximum likelihood estimation– AIC: Akaike information criterion– REML: restricted maximum likelihood– MINQUE: minimum quadratic unbiased estimation– GLS: generalized least squares– OLS: ordinary least squares– PMSE: prediction mean squared error for a kriging predictor– profile likelihood– likelihood ratio test– Vecchia approximation to the likelihood– moment estimation– Fisher information– composite likelihood
Other abbreviations:– i.i.d.: independent and identically distributed– RF: random field– IRF: intrinsic random field– GP: Gaussian process = Gaussian random field– MRF: Markov random field– GMRF: Gaussian Markov random field– SLM: spatial linear model– FT: Fourier transform– IFT: inverse Fourier transform– DFT: discrete Fourier transform– DCT: discrete cosine transform– SPDE: stochastic partial differential equation– RKHS: reproducing kernel Hilbert space
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