Internal tools

shared utilities between GP_deviance and GP_fit

sig_invb(X, Y, beta, corr = list(type = "exponential", power = 1.95),
  nug_thres = 20)

Arguments

X

the (n x d) design matrix

Y

the (n x 1) vector of simulator outputs

beta

a (d x 1) vector of correlation hyper-parameters, as described in corr_matrix

corr

a list of parameters for the specifing the correlation to be used. See corr_matrix.

nug_thres

a parameter used in computing the nugget. See GP_fit.

Value

list with elements delta, L, mu_hat, Sig_invb

Examples

set.seed(3234)
GPfit:::sig_invb(
    X = matrix((0:10) / 10), 
    Y = runif(11), 
    beta = 1.23)
#> $delta
#> [1] 0
#> 
#> $L
#>       [,1]      [,2]      [,3]      [,4]       [,5]       [,6]        [,7]
#>  [1,]    1 0.8265077 0.4789201 0.1972558 0.05815913 0.01233481 0.001888751
#>  [2,]    0 0.5629254 0.7650685 0.5611519 0.26502060 0.08520546 0.019138839
#>  [3,]    0 0.0000000 0.4304715 0.7032249 0.57682708 0.29307495 0.098989250
#>  [4,]    0 0.0000000 0.0000000 0.3894527 0.66934816 0.57151013 0.299219211
#>  [5,]    0 0.0000000 0.0000000 0.0000000 0.38160865 0.65935684 0.566959268
#>  [6,]    0 0.0000000 0.0000000 0.0000000 0.00000000 0.38120819 0.658451478
#>  [7,]    0 0.0000000 0.0000000 0.0000000 0.00000000 0.00000000 0.381179707
#>  [8,]    0 0.0000000 0.0000000 0.0000000 0.00000000 0.00000000 0.000000000
#>  [9,]    0 0.0000000 0.0000000 0.0000000 0.00000000 0.00000000 0.000000000
#> [10,]    0 0.0000000 0.0000000 0.0000000 0.00000000 0.00000000 0.000000000
#> [11,]    0 0.0000000 0.0000000 0.0000000 0.00000000 0.00000000 0.000000000
#>               [,8]         [,9]        [,10]        [,11]
#>  [1,] 0.0002094288 0.0000168577 9.871631e-07 4.213292e-08
#>  [2,] 0.0030477508 0.0003472854 2.849720e-05 1.691769e-06
#>  [3,] 0.0230044707 0.0037516546 4.347645e-04 3.610739e-05
#>  [4,] 0.1032994541 0.0243889531 4.023153e-03 4.700944e-04
#>  [5,] 0.2987956660 0.1037119007 2.458939e-02 4.069131e-03
#>  [6,] 0.5662683994 0.2985371586 1.036620e-01 2.458606e-02
#>  [7,] 0.6584750827 0.5663254062 2.985752e-01 1.036758e-01
#>  [8,] 0.3811331786 0.6584285123 5.663174e-01 2.985842e-01
#>  [9,] 0.0000000000 0.3811270369 6.584169e-01 5.663100e-01
#> [10,] 0.0000000000 0.0000000000 3.811270e-01 6.584171e-01
#> [11,] 0.0000000000 0.0000000000 0.000000e+00 3.811265e-01
#> 
#> $mu_hat
#>           [,1]
#> [1,] 0.7305418
#> 
#> $Sig_invb
#>              [,1]
#>  [1,]   0.0256566
#>  [2,]  -4.6938586
#>  [3,]   9.5504262
#>  [4,]  -3.0967178
#>  [5,] -15.9630542
#>  [6,]  32.0078249
#>  [7,] -31.8570873
#>  [8,]  14.1382504
#>  [9,]   6.4423961
#> [10,] -13.0895363
#> [11,]   6.5357001
#>