PROC SIM2D: Variability at Selected Locations :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The SIM2D Procedure

Example 79.2 Variability at Selected Locations

This example exhibits a more detailed investigation of the variation of simulated Thick values. You use the same thick data set from the section Getting Started: SIM2D Procedure, and you are interested in the simulated values statistics at two selected grid points.

Specifically, you perform a simulation asking for 5,000 realizations (iterations) at two points of the region defined in the section Preliminary Spatial Data Analysis. These are the extreme southwest point and a point toward the northeast corner of the region. Since you do not want to perform the simulation across the whole region, you need to produce a GDATA= data set to specify the coordinates of the selected points. These steps are implemented using the following DATA step and statements:

   data thick;
      input East North Thick @@;
      label Thick='Coal Seam Thickness';
      datalines;
       0.7  59.6  34.1   2.1  82.7  42.2   4.7  75.1  39.5
       4.8  52.8  34.3   5.9  67.1  37.0   6.0  35.7  35.9
       6.4  33.7  36.4   7.0  46.7  34.6   8.2  40.1  35.4
      13.3   0.6  44.7  13.3  68.2  37.8  13.4  31.3  37.8
      17.8   6.9  43.9  20.1  66.3  37.7  22.7  87.6  42.8
      23.0  93.9  43.6  24.3  73.0  39.3  24.8  15.1  42.3
      24.8  26.3  39.7  26.4  58.0  36.9  26.9  65.0  37.8
      27.7  83.3  41.8  27.9  90.8  43.3  29.1  47.9  36.7
      29.5  89.4  43.0  30.1   6.1  43.6  30.8  12.1  42.8
      32.7  40.2  37.5  34.8   8.1  43.3  35.3  32.0  38.8
      37.0  70.3  39.2  38.2  77.9  40.7  38.9  23.3  40.5
      39.4  82.5  41.4  43.0   4.7  43.3  43.7   7.6  43.1
      46.4  84.1  41.5  46.7  10.6  42.6  49.9  22.1  40.7
      51.0  88.8  42.0  52.8  68.9  39.3  52.9  32.7  39.2
      55.5  92.9  42.2  56.0   1.6  42.7  60.6  75.2  40.1
      62.1  26.6  40.1  63.0  12.7  41.8  69.0  75.6  40.1
      70.5  83.7  40.9  70.9  11.0  41.7  71.5  29.5  39.8
      78.1  45.5  38.7  78.2   9.1  41.7  78.4  20.0  40.8
      80.5  55.9  38.7  81.1  51.0  38.6  83.8   7.9  41.6
      84.5  11.0  41.5  85.2  67.3  39.4  85.5  73.0  39.8
      86.7  70.4  39.6  87.2  55.7  38.8  88.1   0.0  41.6
      88.4  12.1  41.3  88.4  99.6  41.2  88.8  82.9  40.5
      88.9   6.2  41.5  90.6   7.0  41.5  90.7  49.6  38.9
      91.5  55.4  39.0  92.9  46.8  39.1  93.4  70.9  39.7
      55.8  50.5  38.1  96.2  84.3  40.3  98.2  58.2  39.5
      ;

   data grid;
      input xc yc;
      datalines;
      0   0
      75  75
   run;

Then, you run PROC SIM2D with the same parameters and characteristics as those in the section Preliminary Spatial Data Analysis. This time, however, you ask for simulated values only at the two locations you specified in the previous DATA step. The following statements execute the requested simulation:

   proc sim2d data=thick outsim=sim1;
      coordinates xc=East yc=North;
      simulate var=Thick numreal=5000 seed=79931
               scale=7.2881 range=30.6239 form=gauss;
      mean 40.1173;
      grid gdata=grid xc=xc yc=yc;
   run;

Once the simulation is performed, summary statistics are computed for each of the specified grid points. In particular, you use PROC UNIVARIATE and a BY statement to request at these locations the quantiles and the extreme observations, as the following statements show:

   proc sort data=sim1;
      by gxc gyc;
   run;
   
   proc univariate data=sim1;
      var svalue;
      by gxc gyc;
      ods select Quantiles ExtremeObs;
      title 'Simulation Statistics at Selected Grid Points';
   run;

The summary statistics for the first grid point (East=0, North=0) are presented in Output 79.2.1.

Output 79.2.1 Simulation Statistics at Grid Point (East=0, North=0)

Simulation Statistics at Selected Grid Points

The UNIVARIATE Procedure

Variable: SVALUE (Simulated Value at Grid Point)

X-coordinate of the grid point=0 Y-coordinate of the grid point=0

Quantiles (Definition 5)
Quantile	Estimate
100% Max	42.1810
99%	41.6986
95%	41.3633
90%	41.1890
75% Q3	40.9044
50% Median	40.5713
25% Q1	40.2191
10%	39.9463
5%	39.7552
1%	39.4201
0% Min	38.7473

X-coordinate of the grid point=0 Y-coordinate of the grid point=0

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
38.7473	2691	42.0656	1149
38.9080	1817	42.0805	3612
38.9449	3026	42.0980	3757
38.9867	2275	42.1782	135
39.0194	3100	42.1810	4536

Finally, Output 79.2.2 displays the summary statistics for the second grid point (East=75, North=75).

Output 79.2.2 Simulation Statistics at Grid Point (East=75, North=75)

Simulation Statistics at Selected Grid Points

The UNIVARIATE Procedure

Variable: SVALUE (Simulated Value at Grid Point)

X-coordinate of the grid point=75 Y-coordinate of the grid point=75

Quantiles (Definition 5)
Quantile	Estimate
100% Max	40.1168
99%	40.1148
95%	40.1134
90%	40.1126
75% Q3	40.1114
50% Median	40.1101
25% Q1	40.1086
10%	40.1075
5%	40.1068
1%	40.1053
0% Min	40.1024

X-coordinate of the grid point=75 Y-coordinate of the grid point=75

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
40.1024	7176	40.1164	8980
40.1029	6262	40.1165	9272
40.1032	7383	40.1167	5676
40.1037	7156	40.1167	6514
40.1037	5643	40.1168	5329

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