Random Walk Wrote:
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> WYB36 Wrote:
> --------------------------------------------------
> -----
> > Yes and no. For complex stachoastic systems,
> we
> > can't reliably predict the behavior of
> individual
> > elements but the overall prediction of the
> system
> > can be accurate. An example might be heat flow.
>
> > We know heat is vibration of individual atoms
> but
> > predicting the position, speed of a particular
> > atom is difficult. But the ensemble results in
> a
> > bulk property known as temperature.
>
> That's not really the type of modelling that I'm
> talking about. I'd consider that more of a
> process model. We're good at that within
> reasonable bounds.
It's not a process model.
> I'm talking more of purely predictive models for
> complex systems. e.g., We know that there's a
> hurricane of some magnitude that's headed in some
> general direction at some relative speed as well
> as other information regarding how hurricanes
> generally work. But knowing the 'bulk properties'
> as you phrase it doesn't provide good predictive
> value to yield an eventual future track. It's
> only when we eliminate most all other
> possibilities along the way that we eventually
> pare uncertainty down to near zero before we start
> to get things right and it's again subject only to
> more straight process-type functions.
The point is that you can't predict street level behavior. You can get a general idea of the path but you aren't going to get a detailed specific path. Again, we simply have a lack of understanding of the problem. That doesn't mean the predictions are completely worthless. The news doesn't help -- They see one track pointing at Virginia and litte Timmy declares a state of emergency. That's why we have multiple models -- Some are better at some aspects of prediction depending on the conditions.
> > And yes, since we tend to model things as
> > differential equations, those equations can
> easily
> > have several different solutions. It may be
> you
> > didn't pick the right solution for the given
> set
> > of initial conditions.
>
> True but again not really what I'm talking about.
> See for example here:
>
>
http://www3.imperial.ac.uk/pls/portallive/docs/1/3
> 9240.PDF
Not surprising. The have injected Guassian noise and can find other local maxima/minima that are reasonably good solutions. There is a similar problem with linear programming. You can find reasonably good solutions to difficult problems in a reasonable amount of time. But to find the "perfect" solution is essentially solving some powerset which is going to take far too long to be useful.
But is the model useless just because it doesn't find the absolute best solution?