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Thus, variability across daily doses has been translated into uncertainty in the
parameter. Although the individual’s true value has no uncertainty, the estimate of
the value has some variability (U.S. Environmental Protection Agency, 1992).
The preceding discussion pertains to the air inhalation for one person. Now
consider a distribution of air inhalation across individuals in a defined population
(e.g., the general U.S. population). In this case, variability refers to the range and
distribution of air inhalation across individuals in the population. Otherwise, uncer-
tainty refers to the exposure assessor’s state of knowledge about that distribution,
or about parameters describing the distribution (e.g., mean, standard deviation,
general shape, various percentiles).
As noted by the National Research Council (1994), the realms of variability and
uncertainty have fundamentally different ramifications for science and judgment.
For example, uncertainty may force decision makers to judge how probable it is that
exposures have been overestimated or underestimated for every member of the
exposed population, whereas variability forces them to cope with a certainty that
different individuals are subject to exposures above and below any of the exposure
levels chosen as a reference point (U.S. Environmental Protection Agency, 1992).
To account for the uncertainty in ERA, process probabilistic models are used.
These techniques generate distributions that describe the uncertainty associated with
the risk estimate (resultant doses). The predicted dose for every 5th percentile to the
95th percentile of the exposed population and the true mean are calculated. Using
these models, the assessor is not forced to rely solely on a single exposure parameter
or the repeated use of conservative assumptions to identify the plausible dose and
risk estimates. Instead the full range of possible values and their likelihood of
occurrence are incorporated into the analysis to produce the range and probability
of expected exposure levels.
In addition to establishing exposure and risk distributions, probabilistic analysis
can also identify variables with the greatest impact on the estimates and illuminated
uncertainties associated with exposure variables through sensitivity analysis. This
provides some insight into the confidence that resides in exposure and risk estimates
and has two important results. First, it identifies the inputs that would benefit most
from additional research to reduce uncertainty and improve risk estimates. Second,
assuming that a thorough assessment has been conducted, it is possible to phrase
the results in more accessible terms, such as, the risk assessment of PCBs in small-
mouth bass is based on a large amount of high-quality reliable data, and we have
high confidence in the risk estimates derived. The analysis has determined that 90%
of the increased cancer risk could be eliminated through a ban on carp and catfish,
but there is no appreciable reduction in risk from extending such a ban to bass and
trout.

5.6 TYPES OF PROBABILITY DISTRIBUTIONS USED

In the MC simulation, new values of the random variables are selected at least 10,000
times and a new estimate of the final damage is foreseen. The results of the calcu-
lations are summarized in a single histogram of damage values; mathematical oper-
ations such as multiplication, exponential functions, matrix calculations, etc. can be

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