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Michael J. Firko and Edward V. Podleckis
the minimum, mean, and standard deviation. Typically, we construct PDFs by
assembling a group of specialists in the appropriate field (e.g., entomology, mycology, plant pathology, virology) to review and discuss the available data. We
use the “expert information” approach described by Kaplan (1992). With this
approach, all pertinent information is shared among the group of specialists before
any estimates are made. This approach increases objectivity and helps avoid
personal ownership of estimates that are made before all pertinent data are shared.
In every biological system, there is uncertainty about pest biology, how well risk
management systems will perform, the level of compliance with the program, and
future ecological and environmental conditions. Uncertainty in estimated values
results from natural biological variation, climate variation, lack of precision in the
model, data gaps, poor data, multiple components in a node, and a variety of other
sources.
The basic approach is to use whatever PDF best represents the available information. It is always tempting to overinterpret available data and specify distributions that are not supported by the data. For example, specification of distributions
such as normal and lognormal requires assumptions concerning the central tendency of the distribution and characteristics of the data and the processes that
generated them. Most risk assessment programs available on the market today
have 20–30 different PDFs from which to choose. However, the following five
are among those chosen most often.
Uniform Distribution
Uniform distributions are the simplest PDF; only a minimum and maximum value
are needed to specify the distribution. Every value between the minimum and
maximum has an equal probability of being selected by the sampling algorithm.
Uniform distributions may be appropriate when there is little justification for
assuming that some values are more likely than others or when data do not suggest
a central tendency. Values beyond the minimum and maximum value are not used
for calculations. Figure 6.3 shows an example of a uniform distribution used in the
assessment for importation of Mexican avocado fruit (USDA 1995c). Uniform
distributions used for probability values that range over an order of magnitude
should be used with caution. If the analysts were thinking on a log scale, results
could be overly conservative. For example, consider a uniform distribution covering two orders of magnitude (minimum = 0.0002, maximum = 0.02). Values
between the minimum and the geometric mean (0.002) will be chosen only about
9% of the time, and values between the geometric mean and the maximum will be
chosen about 91% of the time. Values between 0.01 and 0.02 will be chosen for
about 50% of the calculations.
Triangular Distribution
Triangular distributions are specified by three values: minimum, most likely, and
maximum. The relative frequency of the various values in the distribution is
Michael J. Firko and Edward V. Podleckis
the minimum, mean, and standard deviation. Typically, we construct PDFs by
assembling a group of specialists in the appropriate field (e.g., entomology, mycology, plant pathology, virology) to review and discuss the available data. We
use the “expert information” approach described by Kaplan (1992). With this
approach, all pertinent information is shared among the group of specialists before
any estimates are made. This approach increases objectivity and helps avoid
personal ownership of estimates that are made before all pertinent data are shared.
In every biological system, there is uncertainty about pest biology, how well risk
management systems will perform, the level of compliance with the program, and
future ecological and environmental conditions. Uncertainty in estimated values
results from natural biological variation, climate variation, lack of precision in the
model, data gaps, poor data, multiple components in a node, and a variety of other
sources.
The basic approach is to use whatever PDF best represents the available information. It is always tempting to overinterpret available data and specify distributions that are not supported by the data. For example, specification of distributions
such as normal and lognormal requires assumptions concerning the central tendency of the distribution and characteristics of the data and the processes that
generated them. Most risk assessment programs available on the market today
have 20–30 different PDFs from which to choose. However, the following five
are among those chosen most often.
Uniform Distribution
Uniform distributions are the simplest PDF; only a minimum and maximum value
are needed to specify the distribution. Every value between the minimum and
maximum has an equal probability of being selected by the sampling algorithm.
Uniform distributions may be appropriate when there is little justification for
assuming that some values are more likely than others or when data do not suggest
a central tendency. Values beyond the minimum and maximum value are not used
for calculations. Figure 6.3 shows an example of a uniform distribution used in the
assessment for importation of Mexican avocado fruit (USDA 1995c). Uniform
distributions used for probability values that range over an order of magnitude
should be used with caution. If the analysts were thinking on a log scale, results
could be overly conservative. For example, consider a uniform distribution covering two orders of magnitude (minimum = 0.0002, maximum = 0.02). Values
between the minimum and the geometric mean (0.002) will be chosen only about
9% of the time, and values between the geometric mean and the maximum will be
chosen about 91% of the time. Values between 0.01 and 0.02 will be chosen for
about 50% of the calculations.
Triangular Distribution
Triangular distributions are specified by three values: minimum, most likely, and
maximum. The relative frequency of the various values in the distribution is