# Estimating the Range of Uncertainty in Future Development from Trends in Physical Constants and Predictions of Global Change

### CSIA Discussion Paper 92-06, Kennedy School of Government, Harvard University, July 1992

## Abstract

Science policy frequently hinges on reliable assessment of the uncertainty in predictions
derived from various models. Because of systematic and random errors in the parameters
of scientific models, measured values are commonly considered to be stochastic quantities
following a Gaussian distribution, with the uncertainty characterized by the estimated
standard deviation. We present analysis of multi-decade trends in the reported values of
fundamental physical constants and projections of future energy demand and population
growth, which reveals that a Gaussian, or normal, distribution grossly underestimates the
frequency of events lying very far from the mean. The probability of large deviations is
instead well fit by a simple exponential. This asymptotic behavior appears naturally in a
compound distribution where both the mean and standard deviation are normally distributed
stochastic quantities. We illustrate this formulation by estimating the probability of
catastrophic sea-level rise resulting from global wanning.

#### Keywords: uncertainty analysis, environmental policy, sea-level rise, confidence intervals, scientific models

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