c173c273_lec16_w11[1]

# c173c273_lec16_w11[1] - University of California Los...

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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C173/C273 Instructor: Nicolas Christou Block kriging exampe We will use the 7-point data from earlier lectures. Here they are: s i x y z ( s i ) s 1 61 139 477 s 2 63 140 696 s 3 64 129 227 s 4 68 128 646 s 5 71 140 606 s 6 73 141 791 s 7 75 128 783 Here is the x- y plot: ● ● ● ● ● ● ● ● ● ● ● 62 64 66 68 70 72 74 128 130 132 134 136 138 140 x coordinate y coordinate s1 s2 s3 s4 s5 s6 s7 A B C D For these data, let’s assume that we use the exponential semivariogram model with parameters c = 0 ,c 1 = 10 ,α = 3 . 33, γ ( h ) = 10(1- e- h 3 . 33 ). The corresponding covariance function is: C ( h ) = ( 10 h = 0 10 e- h 3 . 33 h > 1 Suppose we want to estimate the average of the block defined by the coordinates shown on the figure of page 1: (64 , 132) , (64 , 138) , (70 , 132) , (70 , 138) (see figure on page 1). One way to do this is to “krige” many points inside the block and at the end average these esti- mates. Let’s use only 4 points inside the block defined by the following coordinates: A (66 , 134) ,B (66 , 136) ,C (68 , 134) ,D (68 , 136). Predicting point A: W = 10 5 . 103 0 . 435 0 . 199 0 . 489 0 . 259 0 . 048 1 5 . 103 10 0 . 362 0 . 202 0 . 905 0 . 489 0 . 061 1 . 435 0 . 362 10 2 . 902 0 . 199 0 . 111 0 . 362 1 . 199 0 . 202 2 . 902 10 0 . 244 0 . 152 1 . 222 1 . 489 0 . 905 0 . 199 0 . 244 10 5 . 103 0 . 224 1 . 259 0 . 489 0 . 111 0 . 152 5 . 103 10 0 . 193 1 . 048 0 . 061 0 . 362 1 . 222 0 . 224 0 . 193 10 1 1 1 1 1 1 1 1 0 - 1 1 . 196 1 . 334 1 . 985 1 . 497 . 958 . 512 . 388 1 = . 130 . 146 . 240 . 164 . 136 . 072 . 112- 1 . 077 . Therefore, ˆ z ( s A ) = 0 . 130(477)+0 . 146(696)+0 . 240(227)+0 . 164(646)+0 . 136(606)+0 . 072(791)+0 . 112(783) ⇒ ˆ z ( s A ) = 551 . 036. Predicting point B: W = 10 5 . 103 0 . 435 0 . 199 0 . 489 0 . 259 0 . 048 1 5 . 103 10 0 . 362 0 . 202 0 . 905 0 . 489 0 . 061 1 . 435 0 . 362 10 2 . 902 0 . 199 0 . 111 0 . 362 1 . 199 0 . 202 2...
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c173c273_lec16_w11[1] - University of California Los...

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