**Uncertainty Quantification Working Group**

Nov. 29, 11:30 AM, CNLS Conf. Room, TA-3, Bldg. 1690

## Quality assurance methods for probabilistic risk analysis: bounding
exceedance probabilities

Scott Ferson, Applied Biomathematics (scott@ramas.com; www.ramas.com)

### Abstract

Probabilistic risk analysts routinely encounter problems in which they
are faced with non-trivial measurement errors, empirical data with very
small sample sizes, uncertainty about the appropriate shape of the
statistical distributions, unknown dependencies induced by common-cause
or common-mode failures, and possibly doubt about the structural form of
the model itself. Traditional applications of probability theory, often
implemented by Monte Carlo simulation, have usually had to neglect these
kinds of uncertainty, which leads of course to diminished credibility
for the assessments. Approaches involving second-order Monte Carlo
simulation, robust Bayes methods or the theory of imprecise
probabilities have been suggested as computational tools to account for
these uncertainties and assess the reliability of probabilistic risk
analyses, but these approaches are generally computationally intensive
and sometimes theoretically problematic. Probability bounds analysis is
a marriage of probability theory and the techniques of interval analysis
that generalizes and is faithful to both. By focusing on bounding the
cumulative distribution functions characterizing the risk outputs,
probability bounds analysis simplifies the treatment of imprecisely
specified marginal distributions, poorly characterized (or completely
unknown) dependencies and even some aspects of model uncertainty. This
approach allows one to directly compute rigorous and often best-possible
bounds on the probabilities of adverse events and thus provides
estimates of the reliability of a probabilistic risk assessment. It
allows analysts to give quantitative and comprehensive answers to the
"are you sure?" questions about a probabilistic risk assessment.