Floats, precision and probability distributions

[Mike Richardson]

As the debate on the OM representation of floats seems
to have moved in the direction of an encoding which
specifies accuracy, as significant digits or invervals,
may I make a plea that we shouldn't commit to what is
essentially a simplistic view of the *physical* meaning
of a numerical observation, without fully considering
its possible implications.

Any number representing a physical observation is
shorthand for a probability distribution, centred on
the observed value.  Quoting just the measured value is
equivalent to giving only the zeroth moment of the
distribution.

Giving an "accuracy" is equivalent to adding the first
moment of the distribution, but says nothing of the shape
of that distribution - is it rectangular (as quoting
significant digits or an interval tacitly implies),
gaussian, or something else entirely?  Assuming all 
distributions are rectangular makes for (comparatively)
straightforward error analysis, and so is widely used at
present; however, this is only the second step on this
road and it may well be that, in the future, more
sophisticated techniques will utilise more information
about the probability distributions of individual
observations.

I would, therefore, suggest that, if a representation of
reals with a built-in accuracy is added to OM, it should
be done in a manner which is sufficiently open-ended to
allow higher moments of the probability also to be
specified, should that be desired.

Mike Richardson

+--------------------------------------------------------------------+
|                   Dr. Michael Gerard RICHARDSON                    |
|                                                                    |
| Numerical Algorithms Group Ltd.                                    |
| Wilkinson House                      Email:     miker at nag.co.uk    |
| Jordan Hill Road                     Telephone: 01865 511245       |
| Oxford, OX2 8DR, UK                  Fax:       01865 311205       |
+--------------------------------------------------------------------+

Any opinions expressed here are purely my own.