Optimized sample variance

Draws an optimal sample that minimizes or maximizes the sample variance

optimized.sample.variance(x, n, type = "maximized")

Arguments

x	A vector to draw a sample from
n	Number of samples to draw
type	Type of sample variance optimization c("maximized", "minimized")

Value

A data.frame with "idx" representing the index of the original vector and "y" is the value of the sampled data

Author

Jeffrey S. Evans <jeffrey_evans@tnc.org>

Examples

 library(sp)
   data(meuse)
   coordinates(meuse) <- ~x+y

 n = 15
 # Draw n samples that maximize the variance of y
 ( max.sv <- optimized.sample.variance(meuse$zinc, 15) )
#> 
#> maximized sample variance: 568741.542857143
#>    idx    y
#> 1   54 1839
#> 2  107  113
#> 3  106  117
#> 4   82 1672
#> 5   68  119
#> 6   59 1571
#> 7  127  119
#> 8   53 1548
#> 9  131  126
#> 10  55 1528
#> 11 113  128
#> 12 137  129
#> 13  40 1454
#> 14 108  130
#> 15  80 1383
 
 # Draw n samples that minimize the variance of y
 ( min.sv <- optimized.sample.variance(meuse$zinc, 15, 
               type="minimized") )
#> 
#> minimized sample variance: 1795.17142857143
#>    idx   y
#> 1  145 471
#> 2  130 474
#> 3   47 464
#> 4  139 451
#> 5  152 496
#> 6   14 504
#> 7   88 505
#> 8   57 432
#> 9   89 420
#> 10 129 415
#> 11   8 406
#> 12 144 403
#> 13  22 402
#> 14  91 400
#> 15  50 375
 
 # Plot results
 plot(meuse, pch=19, col="grey")
   plot(meuse[max.sv$idx,], col="red", add=TRUE, pch=19)
     plot(meuse[min.sv$idx,], col="blue", add=TRUE, pch=19)
     box()
     legend("topleft", legend=c("population","maximized variance", 
            "minimized variance"), col=c("grey","red","blue"),  
            pch=c(19,19,19))

# \donttest{
 # Raster example (not memory safe) 
 library(raster)
   r <- raster(system.file("external/test.grd", package="raster"))
  
# Calculate optimal sample variance and coerce to SpatialPointDataFrame 
#   using xyFromCell
     ( min.sv <- optimized.sample.variance(getValues(r), n, type="minimized") )
#> 
#> minimized sample variance: 0.781294194342835
#>     idx        y
#> 1  4517 425.4702
#> 2  4592 425.2701
#> 3  2063 424.9967
#> 4  7080 424.8377
#> 5  7734 425.8081
#> 6  7929 426.0826
#> 7  7295 426.3960
#> 8  8580 426.3975
#> 9  3019 426.5510
#> 10 4287 426.5703
#> 11 2222 426.8780
#> 12 6660 426.8993
#> 13 6931 427.4153
#> 14 7448 427.5166
#> 15 7159 427.5213
      min.sv <- sp::SpatialPointsDataFrame(xyFromCell(r, min.sv[,"idx"], 
                                           spatial=TRUE), data=min.sv) 
     ( max.sv <- optimized.sample.variance(getValues(r), n) )
#> 
#> maximized sample variance: 517250.482316504
#>     idx         y
#> 1  3639 1736.0580
#> 2  5888  138.7071
#> 3  5968  148.7244
#> 4  3719 1648.3469
#> 5  5251  152.5585
#> 6  7483 1488.6211
#> 7  5331  152.7412
#> 8  3562 1483.9067
#> 9  5885  152.9692
#> 10 7563 1481.8656
#> 11 6287  157.3041
#> 12 7484 1468.7628
#> 13 5887  159.4636
#> 14 7564 1463.7230
#> 15 6352  160.1675
      max.sv <- sp::SpatialPointsDataFrame(xyFromCell(r, max.sv[,"idx"], 
                                           spatial=TRUE), data=max.sv)

 plot(r)
   plot(max.sv, col="blue", add=TRUE, pch=19)
   plot(min.sv, col="red", add=TRUE, pch=19)
   box()
 legend("topleft", legend=c("maximized variance", "minimized variance"),
        col=c("red","blue"), pch=c(19,19))
 # }