Random algorithm

[François Chaplais]

Le 13 nov. 08 à 19:35, Randall Reetz a écrit :

> Thank you Francois,
>
> Can statistics be rigorously derived from proability math?  I hope so.
yes, that is the "clean" way, which is, by the way, the best suited  
for academic teaching.

> Both are heavily dependent on what appears to be statistics ("both"  
> refers here to my twin gods).  I am a self admitted thermodynamics  
> and information science freak.  I'd hate to think that my whole  
> world was anecdotally argued.  I do see a strange but familiar  
> symmetry between the finite/infinite distinction that seperates  
> probability theory and practice, and the open/closed system maths  
> that seperates the thermodynamic engineering from pure science.
>
> Randall
>

I dug up my old textbooks on statistical physics (which is another  
word for thermodynamics) and the textbook is entirely based on  
probabilistic methods. The official motivation for statistical physics  
is that, for "macroscopic" systems, the behaviour of" individual"  
elements are not observable, so you only have access to their  
statistics.

I won't digress more on this subject, as it is OT. Just one last word:  
even in you stick to deterministic models, sampling, aka A/D  
converters, is a tricky issue, for reasons which are similar to  
experiments on probabilistically modeled systems: the data set that is  
accessible to you is of measure zero with respect to the (hidden) set  
of data that lives in the model. In practice, unless you enforce  
stronger assumptions on the model, there is now way to bring  
contradiction to the mathematical model by means of a suitable  
experiment.

Now, back to rev...

cheers
	François