Spatial Process Estimates - IMAGe

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A Normal World We assume that g(x) is a Gaussian process, ρk(x, x ′ ) = COV (g(x), g(x ′ )) For the moment assume that E(g(x)) = 0. (A Gaussian process ≡ any subset of the field locations has a multivariate normal distribution. ) We know what we need to do! If we know k we know how to make a prediction at x! ĝ(x) = E[g(x)|data] i.e. Just use the conditional multivariate normal distribution. 4
A review of the conditional normal and u ∼ N(0, Σ) u = ( u1 u 2 ) ( ) Σ11 , Σ Σ = 12 Σ 21 , Σ 22 [u 2 |u 1 ] = N(Σ 2,1 Σ −1 1,1 u 1, Σ 2,2 − Σ 2,1 Σ −1 1,1 Σ 1,2) (distribution of u 2 given u 1 ) 5
Page 1 and 2: Spatial Process Estimates SAMSI Sum
Page 3: The additive model Given n pairs of
Page 7 and 8: The Kriging weights Conditional dis
Page 9 and 10: My geostatistics/BLUE overhead For
Page 11 and 12: BLUE/Universal Kriging Find d by Ge
Page 13 and 14: The spline connection Basis functio
Page 15 and 16: Identifying a covariance function T
Page 17 and 18: Correlations among ozone In many ca
Page 19 and 20: 50 Sensitivity to the covariance Ex
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Spatial Process Estimates - IMAGe

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