information about the population that uncertainty can be
quantified. This assumption is common to multiple regression
where practitioners are concerned with predicting values be-
yond the values in the sample dataset (Weisberg, 1985). Also,
our approach assumed a random equal probability sample of
the underlying populations. Modifications to the bootstrap
protocol would be needed for other sampling schemes such as
stratified random sampling.
Our case example was based on masking out areas that
were likely to have 0 percent tree canopy cover in a portion
of Georgia. Our technique offers a straightforward way to ac-
complish this however; masking procedures that only operate
on part of the distribution may increase other types of errors.
For example, the original percent tree canopy cover had an
error rate of 0.2 percent (predicting 0 percent tree canopy
cover when the true value was >0 percent). The masking
procedure increased this error rate to 9.7 percent. Decisions
to mask final products should be made with caution. Masking
procedures may decrease some error rates while at the same
time increasing other error rates, as is the case here. Further,
if a model was originally unbiased (e.g., mean error = 0) then
manipulating predictions in one part of the distribution will
result in overall bias (mean error
≠
0).
The ability to obtain a spatially-explicit understanding
of uncertainty and error of predictions provides valuable
information for any application where continuous variable
mapping is desired. For complex spatial models, such as the
LANDFIRE
Prototype Project referred to previously (Rollins and
Frame, 2006), this information can be used to understand the
sensitivity of the modeled fire output and help to define the
conditions for which model outputs are most reliable. Fur-
ther, maps of uncertainty and error can inform field validation
efforts, which could significantly reduce costs of monitoring
efforts. One example of this would be in the design of sam-
pling schemes to validate models of above ground biomass
in remote areas such as Alaska or some areas in the tropical
rainforests, where permanent inventory plots are lacking.
Conclusions
Uncertainty remains an important subject area in remote sens-
ing, but the tools used to quantify uncertainty must keep pace
Plate 2. Top Row: observed values versus the random forest predicted values for each population. The shading of light gray to black
denotes the density of predicted values where the observed value was inside the 95 percent prediction interval. The red dots denote
observed values that where outside the 95 percent prediction interval. Middle Row: histogram of predicted values from the Monte Carlo
error assessment. Bottom Row: the percent of observed values within the 95 percent prediction interval in each population. The red line
denotes 95 percent in the prediction interval, the solid blue lines denotes minimum and maximum predicted values in the Monte Carlo
assessment, and the dashed blue lines represent the 99 percent quantile of predicted values in the Monte Carlo assessment.
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