# Uncertainty Estimates in Scientific Models: Lessons from Trends in Physical Measurements, Population and Energy Projections

*Uncertainty Modeling and Analysis: Theory and Applications*, B.M.Ayyub and M.M. Gupta (Editors), North-Holland-Elsevier Scientific Publishers, 1994

## Abstract

Results of a systematic analysis of actual vs. estimated uncertainty in scientific
models are presented. Data sets include: i) time trends in the sequential measurements
of the same physical quantity; ii) national population projections; iii) projections for
the United States' energy sector. Probabilities of large deviations from the true
values are parametrized by an exponential distribution with the slope determined by
the data. An alternative parametrization by Levy stable distributions, based on the
fractal model for the distribution of errors, is described. In practice, one can
hedge against unsuspected uncertainties by inflating the reported uncertainty range
by a default safety factor determined from the relevant historical data sets. This
empirical approach can be used in the uncertainty analysis of the
low probability/high consequence events (such as risk to public health from exposure to
electromagnetic fields or risk of extreme sea-level rise resulting from global warming).

#### Keywords: uncertainty, systematic errors, physical measurements, population projections, energy projections

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