8/20/2019 Geomatematika 4 Cross Validasi

1/21

8/20/2019 Geomatematika 4 Cross Validasi

2/21

8/20/2019 Geomatematika 4 Cross Validasi

3/21

The $64 question : does geostatistics work?

Data:The grades of 64 blocks of size 1 x 1

This exercise has been designed to highlight the economic impact of estimation errors.

8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

1 2 3 4

4

3

2

1

8/20/2019 Geomatematika 4 Cross Validasi

4/21

The $64 question : does geostatistics work?

Data:The grades of 64 blocks of size 1 x 1were available in an area 8 x 8

8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

1 2 3 4

4

3

2

1

8/20/2019 Geomatematika 4 Cross Validasi

5/21

The $64 question : does geostatistics work?

Data:The grades of 64 blocks of size 1 x 1were available in an area 8 x 8

Shows 16 of these grades

8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

1 2 3 4

4

3

2

1

8/20/2019 Geomatematika 4 Cross Validasi

6/21

The $64 question : does geostatistics work?

Data:The grades of 64 blocks of size 1 x 1were available in an area 8 x 8

Shows 16 of these grades

Each from the top left corner of a

block of size 2 x 2

8 7 6 5 4 3 2 1

735 45 125 167   1

2

450 337 95 245   3

4

124 430 230 460   5

6

75 20 32 20   7

8

1 2 3 4

4

3

2

1

8/20/2019 Geomatematika 4 Cross Validasi

7/21

The $64 question : does geostatistics work?

Data:The grades of 64 blocks of size 1 x 1were available in an area 8 x 8

Shows 16 of these grades

Each from the top left corner of a

block of size 2 x 2

The values of the other 48 samples

will be used later for comparison

purposes

8 7 6 5 4 3 2 1

735 45 125 167   1

2

450 337 95 245   3

4

124 430 230 460   5

6

75 20 32 20   7

8

1 2 3 4

4

3

2

1

8/20/2019 Geomatematika 4 Cross Validasi

8/21

The $64 question : does geostatistics work?

Polygonal Estimation  8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

4

3

2

1

1

124

3 4

735 45 125 167

450 337 95 245

2

430 230 460

75 20 32 20

8/20/2019 Geomatematika 4 Cross Validasi

9/21

8 7 6 5 4 3 2 1

735 45 125 167   1

2

450 337 95 245   3

4

124 430 230 460   5

6

75 20 32 20   7

8

1 2 3 4

4

3

2

1

The $64 question : does geostatistics work?

Coba anda lakukan Estimasi

menurut ‘perasaan’ saudara??

8/20/2019 Geomatematika 4 Cross Validasi

10/21

The $64 question : does geostatistics work?

Kriging Estimation  8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

1

189

99 81

4

3

2

1 88 125

3 4

442 190 142 204

354 276 212 279

2

226 216 271

8/20/2019 Geomatematika 4 Cross Validasi

11/21

The $64 question : does geostatistics work?

Selective Mining

8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

4

3

2

1

1

124

3 4

735 45 125 167

450 337 95 245

2

430 230 460

75 20 32 20

Suppose that in this case the economic cutoff  is 300.

So the expected profit is:

735 + 450 + 337 + 430 + 460 – (5 x 300) = 912

Estimation Polygonal

8/20/2019 Geomatematika 4 Cross Validasi

12/21

8/20/2019 Geomatematika 4 Cross Validasi

13/21

The $64 question : does geostatistics work?

Selective Mining8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

44 155

3 4

505 143 88 207

270 328 171 411

2

220 154 263

101 54

4

3

2

1

1

102

Cutoff is 300.

Expected profit(Polygonal): 912

True ValueActual profit

would be: 86

8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

4

3

2

1

1

124

3 4

735 45 125 167

450 337 95 245

2

430 230 460

75 20 32 20

8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

88 125

3 4

442 190 142 204

354 276 212 279

2

226 216 271

99 81

4

3

2

1

1

189

Expected profit

(Kriging): ???

8/20/2019 Geomatematika 4 Cross Validasi

14/21

The $64 question : does geostatistics work?

Selective Mining8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

44 155

3 4

505 143 88 207

270 328 171 411

2

220 154 263

101 54

4

3

2

1

1

102

Cutoff is 300.

Expected profit(Polygonal): 912

True ValueActual profit

would be: 86

8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

4

3

2

1

1

124

3 4

735 45 125 167

450 337 95 245

2

430 230 460

75 20 32 20

8 7 6 5 4 3 2 1

1

2

3

4

5

6

7

8

88 125

3 4

442 190 142 204

354 276 212 279

2

226 216 271

99 81

4

3

2

1

1

189

Expected profit

(Kriging):

442 + 354 + 276 + 226 +

271 – (5 x 300) = 69

Estimasi ANDA???

8/20/2019 Geomatematika 4 Cross Validasi

15/21

The $64 question : does geostatistics work?

Selective Mining

8/20/2019 Geomatematika 4 Cross Validasi

16/21

Studi Kasus

8/20/2019 Geomatematika 4 Cross Validasi

17/21

SEAM BATUBARA

8/20/2019 Geomatematika 4 Cross Validasi

18/21

Jenis blok:blok regular rectangular grid,unreguler single hole

Jumlah Blok yang dihitung:720 buah

8/20/2019 Geomatematika 4 Cross Validasi

19/21

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

     K    e    t    e     b    a     l    a    n

     B    a    t    u     b    a    r    a     E    s    t     i    m    a    s     i     I     D     S     (    m

     )

Ketebalan Batubara (m)

8/20/2019 Geomatematika 4 Cross Validasi

20/21

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

     K    e    t    e     b    a     l    a    n     B    a    t    u     b

    a    r    a     E    s    t     i    m    a    s     i     O    r     d     i    n    a    r    y     K    r     i    g

     i    n    g     (    m     )

Ketebalan Batubara (m)

8/20/2019 Geomatematika 4 Cross Validasi

21/21