Re: xml support in context / mathml

[Johannes Huesing <hannes@ruhrau.de>]

On Mon, Jan 22, 2001 at 04:54:19PM +0100, Hans Hagen wrote:
> 
> Somehow, when i look at the specs, i cannot get by the feeling that some
> important aspects have been overlooked -) 
> 

Hi Hans and all,

I skimmed the examples in the MathML manual (which Hans distributed
some printed copies of during the Dante meeting) and I have some
remarks regarding the statistics examples on pp. 131 to 134.

In the examples empirically gained values and their expectations are
mistaken for one another. The first example (which spells in TeX as
$\bar{x} = \frac1n\sum x_i$) is ok (the mean being the sum of the
values over the observations divided by the number of obs). Statistic
2 is not really wrong
($\sigma(x)\approx\sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}$) but a bit
weak: I would take the expectation of the right expression and put an
equal sign between the two expressions. For statisticians, there is
definitely the need for an <expectation> element which would spell as
an upright E which is strongly right associative so you could drop the
parentheses around the X in E(X) or in E(sin X) (although I would rather
put the parentheses around here) but not in E(XY). Physicists would
put angle brackets around the argument and drop the E so the
expectation tag is not uninteresting.

The third example is plain wrong as it really messes up the
theoretical value "variance" $\sigma^2 =
\expectation((X-\expectation(X))^2)$ and its unbiased estimate $s^2$,
which is equal to the term on the right (the square of the right
expression in example 2) but only approxiamtely equal to the
expression in the middle (so you have to swap the \approx and the = in
the example). Moreover, I find the notation of overbarring a whole
expression unusual (and inconsistent with the i index since you don't
write $\bar{x}_i$ either) but I do not know of a notation other than
$\frac1n\sum\cdots$ for that. And this notation has the disadvantage
that it had to be flexible wrt the number of observations (n here).  

And thank you very much for the lift back to Duisburg: I managed to
make it home from there before Linux was updated on the laptop
:-). Hope you made it home safely.

Greetings

Johannes
-- 
"Human Genome" may be a binary file. See it anyway?