PREDICTIONS – 10 Years Later - Santa Fe Institute

APPENDIX B
Expected Uncertainties on S-Curve Forecasts
Alain Debecker and I undertook an extensive computer simulation, (a
Monte Carlo study) to quantify the uncertainties on the parameters determined
by S-curve fits. 1 We carried out a large number of fits,
(around forty thousand), on simulated data randomly deviated around
theoretical S-curves and covering a variety of time spans across the
width of the life cycle. We fitted the scattered data using Equation (2)
from Appendix A with the constant b replaced by at o so that t o has the
units of time. Each fit yielded values for the three parameters M, a, and
t o . With many fits for every set of conditions, we were able to make
distributions of the fitted values and compare their average to the theoretical
value used in generating the scattered data. The width of the
distributions allowed us to estimate the errors in terms of confidence
levels.
The results of our study showed that the more precise the data and
the bigger the section of the S-curve they cover, the more accurately
the parameters can be recovered. I give below three representative
look-up tables. From Table II we can see that historical data covering
the first half of the S-curve with 10 percent error per data point will
yield a value for the final maximum accurate to within 21 percent, with
a 95 percent confidence level.
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