Re: [Bug-gnubg] Re: Rollout jsd, statsig etc. [LONG]

[Massimiliano Maini]

Hmm maybe it's just too complicate for me.

It seems to me that the vectors you update at each iteration contain
the probability distribution function of the "equity" of each play, somehow
estimated from rollout results up to the current trial. At the end, you
just integrate on the multivariate tail to compute "your" probability.

If the above is true, on top of assuming a uniform prior, you assume
that the real pdf are the ones you have on your last step.
This is not far from assuming that the real equities are the estimated
ones. Duh, I must be missing something ...

MaX.

2009/11/17 Timothy Y. Chow <address@hidden>:
> On Tue, 17 Nov 2009, Massimiliano Maini wrote:
>> 2009/11/16 Timothy Y. Chow <address@hidden>:
>> > The multivariate tail probability, for
>> > example, tells you only the probability that some strange event will occur
>> > *under the assumption that the equities are equal to the estimated
>> > equities*.  This is *not* the same as *the probability that the true
>> > equities are different from their estimated values*.
>>
>> Just for my understanding, the bayesian approach would be no different
>> with respect to that, right ?
>>
>> It will give you a probability that some strange event will occur under
>> the assumption that the estimated pdf are the ones you have on the
>> current trial/iteration (plus the initial assumption on those pdf),
>> right ?
>
> No.  Under the Bayesian approach, the reported probability that (for
> example) Play A is the best is the probability that Play A is the best,
> *assuming* that the equities of the various plays were all chosen
> uniformly at random before you saw any rollout results.  (I'm assuming you
> pick a uniform prior.)
>
> Here, the "strange event" you're measuring is, "the equity really was
> something very different from the estimated equity, yet somehow we managed
> to see these very non-representative results."  It should be clear that
> measuring this event is more meaningful than *assuming* that the true
> equity is the estimated equity, and computing the probability that you
> will get misleading results in the future.  If you're going to *assume*
> that the true equity is the estimated equity, why would you roll things
> out further?  What you're interested in is the possibility that the true
> equity is *not* the estimated equity, so you shouldn't *assume* that
> they're equal.