[EM] Exact spatial model probabilities?

[Forest Simmons]

I'm thinking ergodic theory.... here's a relevant quote from the wikipedia
article:

The concepts of ergodicity <https://en.m.wikipedia.org/wiki/Ergodicity> and
the ergodic hypothesis <https://en.m.wikipedia.org/wiki/Ergodic_hypothesis> are
central to applications of ergodic theory. The underlying idea is that for
certain systems the time average of their properties is equal to the
average over the entire space.

We have the force field, and I proposed using it to find sinks as possibly
stable equilibria positions ... local minima of the electo-potential V.

All we have to do is add some inertia to the test point and set it in
motion. Then keep track of the time average, and we have a space average
for the basin to which the particle is limited by its initial energy.




El mar., 25 de ene. de 2022 3:20 p. m., Daniel Carrera <dcarrera at gmail.com>
escribió:

>
>
> On Tue, Jan 25, 2022 at 5:10 PM Daniel Carrera <dcarrera at gmail.com> wrote:
>
>> The total number of operations is V*C^2 which... can be a lot if V is
>> large. But it might not be too bad if the alternative way of computing the
>> volume of 1 set of preferences costs more than doing a simple {A,B}
>> comparison V times. There might be some clever geometrical tricks to
>> quickly classify some of the voters, but I can't think of any right now
>> that is obviously faster.
>>
>
> To expand a little bit: If you have C candidates you have C! possible
> orderings. Whereas the partitioning idea only requires C^2 candidate pairs
> {A,B}. Perhaps a dumb {A,B} comparison performed V times is cheaper than a
> clever volume-finding algorithm performed C! times.
>
> --
> Dr. Daniel Carrera
> Postdoctoral Research Associate
> Iowa State University
>
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