Prediction using probability density functions

From: Joel Pitt (
Date: Wed May 03 2006 - 15:45:09 MDT

It occured to me, while reading the discussion on our ability to make
predictions of future technology, that we should use probability
density functions (PDFs) to make educated guesses. Especially when
several intermediary technologies are needed to reach the final
prediction, in which case the PDF for each technology or milestone on
the way can be chained together to create a final PDF for when the
final prediction will occur.

At a very rough guess I would say the PDF for the occurence of the
singularity could resemble something like a Gamma distribution
( with k=3, theta=2.
I.e. there is a peak region of time that we have some expectation the
singularity will occur but the distribution is stretched into the
future indicating possibility that it could be delayed for sometime.

Actually I think a PDF with a much longer/fatter tail would be more
appropriate as this could represent future low probability points of
singurity occurence if a cataclysmic event occurs in the mean time
(although if you are cynical and think cataclysm is more likely than
us seeing singularity then you'd probably reflect the the PDF.

The benefit here is that PDFs can convey alot more about our
(un)certainty of future events. The negative is that the selection of
such distributions is still rather arbitrary.

Just my 2 cents. For those that think we have no ability to make
predictions then that equates to a uniform distribution ranging from
now to the end of the universe ;P


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