Transcript GRTS for the Average Joe: A GRTS Sampler for Windows

WEST, Inc.
GRTS for the Average Joe: A
GRTS Sampler for Windows
Trent McDonald
Monitoring Science Symposium
Denver, CO
21-24 Sep 2004
Outline
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Motivation for the GRTS sampler
Description of the sampler, S-Draw
Examples
Performance
Planned modifications
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Motivation
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• Basic hypotheses:
– Average Joe understands the utility of GRTS
samples
– Average Joe does not totally understand the
inner workings of GRTS sampling
– Average Joe could not draw a GRTS sample if
his life depended on it.
Motivation
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• A GRTS sampler was needed because:
– Average Joe should be able to draw GRTS
samples
– I should be able to draw GRTS samples
S-Draw
• Windows application
• Written in Fortran 95
– Amazing speed
– Cross-platform portability
ok
– Cross-language calls easy
(S-Plus, R, C++)
• Used Lahey compiler
• Also S-DrawB
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S-Draw
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• Draws samples of
– Discrete units (finite populations)
– Located in either 1-D or 2-D
• Examples:
– 1-D: River segments located by river mile
– 2-D: Grid cells located in an area
– 2-D: River segments located by coordinates of
their midpoints
S-Draw
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• Coordinates of units are specified in a
text file
– i.e., the sampling frame is a ASCII file
• Sampling frame can optionally contain
weights and ID’s
S-Draw
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• Frame Formats:
Sample Structure
Predefined
Data Included in Frame
Sample
weights
Coordinates
ID's
Order of fields in
frame file
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
No
Yes
x wgt id
x wgt
x id
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
Yes
Yes
No
No
Yes
Yes
No
No
No
Yes
Yes
No
No
Yes
Yes
Yes
Yes
-
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
x
wgt id
wgt
id
[# lines counted]
x y wgt id
x y wgt
x y id
xy
k1 … kK wgt id
k1 … kK wgt
k1 … kK id
k1 … kK
1-D
2-D
Yes
Yes
Yes
Yes
Yes*
Yes*
Yes*
Yes*
*K
specified on the first line of the frame file
S-Draw
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• Example frame: Eagle study
STARTPNT_X
STARTPNT_Y
LINE_ID
ID
ENDPNT_X
ENDPNT_Y
-421014
4572670
1
439
-420245
4572670
-421295
4574670
2
440
-419802
4574670
-421245
4576670
3
441
-419802
4576670
-421196
4578670
4
442
-419802
4578670
-421292
4580670
5
443
-419802
4580670
-421687
4582670
6
444
-419802
4582670
-422806
4584670
7
445
-419802
4584670
-423122
4586670
8
446
-419802
4586670
-422972
4588670
9
447
-419802
4588670
-422836
4590670
10
448
-419802
4590670
-422352
4592670
11
449
-419802
4592670
-421284
4594670
12
450
-419802
4594670
Columns following
frame data ignored
S-Draw
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• Does the quadrant-recursive mapping
of Stevens and Olsen (2004):
2
4
n
0
1
3
2
4
1
4 3 1 2
1
3
4
2
3
S-Draw
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• Pixelsize = size of smallest quadrant in
recursive map
• S-Draw allows user to specify
pixelsize
S-Draw
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• Line segment (0,n] sampled using a
systematic sample
– Random start between (0,1]
– Step size = 1.0
Random start = 0.19
0
2
1
u1
u2
u3
3
u4
n
S-Draw
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• Reverse-hierarchical ordering of
sample optionally applied
–
–
–
–
Convert sample order to base-4: 10010=012004
Reverse base-4 digits: 012004=002104
Convert back to base-10: 002104=3610
Sort sample on base-10 numbers
S-Draw
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• Users can pre-define the hierarchical
sort keys
• Digits within each level of the
hierarchy are randomly permuted, and
sample is drawn as usual
• Allows use of a general recursive map
– Triangular-recursive
– ID’s like: state.county.watershed.segment
S-Draw
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• Triangular-recursive mapping:
1
2
4
3
Examples
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• C:\>s-drawb –n 20 –popsize 100
– Will produce 1-D GRTS sample of size 20 assuming
units are located at coordinates 1, 2, …, 100
• C:\>s-drawb –n 20 –popsize 100 –pixelsize 100
– Will produce a simple random sample of size 20
• C:\>s-drawb –n 20 –popsize 100 –nrand
– Will produce a fixed-size systematic sample
Examples
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• Golden eagle sample:
– Dense grid of transect start points spaced 2km
north-south, 100km east-west
– “No-fly” transect portions eliminated, new
transect start created
– Frame:
• 27,078 starting points over western US
• 2-D coordinates and ID’s
– Desire sample of 416 transects
• 208 primary, 208 alternate
Examples
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Coordinates and ID in frame
2-D
Frame
file
Sample size
Examples
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Performance
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• GRTS sample of size 500 from
100,000 took 4.2 seconds on my laptop
• GRTS sample of size 500 from
1,000,000 took 44.3 seconds
• Algorithms approximately O(N)
• Runs should take ~ 4.45e-5(N) seconds
– N=5,000,000: ~3.7 minutes
Enhancements
• An S-Plus and R interface
• Ability to read .e00 file, and ArcGIS
binary files
• Ability to take a true point sample
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