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Michael J. Firko and Edward V. Podleckis
probability. In simple quantitative assessments, point estimates are used to calculate estimates of risk (a single number resulting from a single calculation), and
estimates are expressed in quantitative terms such as “a probability of 0.01.”
Usually, the point estimate represents a best estimate. However, quantitative
assessments that rely on point estimates can neither account explicitly for uncertainty in the estimated input values nor can they express uncertainty in the final
risk estimate.
The primary reason for conducting a probabilistic assessment is to provide a
definitive mechanism to account for the uncertainty in the model inputs. Examples of “bad events” (risk assessment endpoints) include the frequency or probability of contamination, pest entry, pest establishment, or pest outbreaks. For most
of these probabilistic risk assessments, the bad event—the endpoint of the risk
assessment—is the frequency of pest establishment. Our probabilistic risk assessments have four basic steps: (1) scenario analysis, (2) development of the mathematical model, (3) construction of probability density functions as model inputs,
and (4) Monte Carlo simulations.
Scenario Analysis and Development of a
Mathematical Model
Scenario analysis is essentially model building; the risk scenario represents a risk
model. Our scenario analyses involve identifying the events (nodes) that must
occur before some “bad outcome” can result. The scenario provides a visual
representation of the risk model. The nature of the scenario dictates the appropriate mathematical model to use for risk calculations. For example, if all nodes are
independent and if each of the events must occur before the endpoint can be
reached, the appropriate mathematical model is a simple, linear, multiplicative
model.
Figure 6.1 shows the scenario used in the Mexican avocado risk assessment
(USDA 1995c), a simple, linear, multiplicative model. The nodes shown for
program option A (imports with no additional risk mitigations beyond those
already in place) are the same as for program option B (a specific systems
approach for risk mitigation). Both scenarios are displayed to show node designations that are useful for keeping track of the progress of the subsequent calculations. The models used in the Karnal Bunt assessments are similar to but more
complex than those shown for the Avocado assessment. When events (primary
nodes) can occur as a result of more than one event (subnodes), the model
becomes more elaborate as illustrated in Figure 6.2 by a scenario from one of the
Karnal Bunt risk assessments (USDA 1996a). Note that in this scenario, although
the primary nodes share a simple, linear, multiplicative relationship, some of the
primary nodes are composed of multiplicative and additive subnodes and subsubnodes.
In the Japanese Unshu orange assessment (USDA 1995b), four scenarios representing four different program options were examined. In the risk assessments for
Michael J. Firko and Edward V. Podleckis
probability. In simple quantitative assessments, point estimates are used to calculate estimates of risk (a single number resulting from a single calculation), and
estimates are expressed in quantitative terms such as “a probability of 0.01.”
Usually, the point estimate represents a best estimate. However, quantitative
assessments that rely on point estimates can neither account explicitly for uncertainty in the estimated input values nor can they express uncertainty in the final
risk estimate.
The primary reason for conducting a probabilistic assessment is to provide a
definitive mechanism to account for the uncertainty in the model inputs. Examples of “bad events” (risk assessment endpoints) include the frequency or probability of contamination, pest entry, pest establishment, or pest outbreaks. For most
of these probabilistic risk assessments, the bad event—the endpoint of the risk
assessment—is the frequency of pest establishment. Our probabilistic risk assessments have four basic steps: (1) scenario analysis, (2) development of the mathematical model, (3) construction of probability density functions as model inputs,
and (4) Monte Carlo simulations.
Scenario Analysis and Development of a
Mathematical Model
Scenario analysis is essentially model building; the risk scenario represents a risk
model. Our scenario analyses involve identifying the events (nodes) that must
occur before some “bad outcome” can result. The scenario provides a visual
representation of the risk model. The nature of the scenario dictates the appropriate mathematical model to use for risk calculations. For example, if all nodes are
independent and if each of the events must occur before the endpoint can be
reached, the appropriate mathematical model is a simple, linear, multiplicative
model.
Figure 6.1 shows the scenario used in the Mexican avocado risk assessment
(USDA 1995c), a simple, linear, multiplicative model. The nodes shown for
program option A (imports with no additional risk mitigations beyond those
already in place) are the same as for program option B (a specific systems
approach for risk mitigation). Both scenarios are displayed to show node designations that are useful for keeping track of the progress of the subsequent calculations. The models used in the Karnal Bunt assessments are similar to but more
complex than those shown for the Avocado assessment. When events (primary
nodes) can occur as a result of more than one event (subnodes), the model
becomes more elaborate as illustrated in Figure 6.2 by a scenario from one of the
Karnal Bunt risk assessments (USDA 1996a). Note that in this scenario, although
the primary nodes share a simple, linear, multiplicative relationship, some of the
primary nodes are composed of multiplicative and additive subnodes and subsubnodes.
In the Japanese Unshu orange assessment (USDA 1995b), four scenarios representing four different program options were examined. In the risk assessments for