Pat wrote:
> Hello,
>
> Say you use a Monte Carlo process to get a confidence interval.
> Rather than running 100 iters (or 1000, or whatever) and settling
for
> a fixed p, the idea is to get an arbitrary p value.
>
> So you iterate ad infinitum. As you go, the p goes down, and the
> interval gets wider. Say you have a measured value, which initially
> lies outside the interval. You iterate the MC until it becomes so
> wide it encompasses your value. You then have a p of < 1/(n-1)
where
> n is the # of iterations it took to make the interval this large.
>
> I have a gut feeling something is wrong here. It seems a bit too
> "sporty", a procedure that lets you dial up any desired p value is
> suspect. However, I can't put my finger on why it is wrong.
>
> Any ideas?
>
> Pat
To "get an arbitrary p value", most people would want to convert this
question into one where you are attempting to estimate the probability
of an event whose true value is roughly p, and where you want the
estimate of the probability to be good to within a certain accuracy
... for example the estimate might need to have a standard deviation
of
0.1 times the smaller of p and (1-p). Then assuming your simulations
are equivalent to binomial sampling with sample size N, you get an
equation (determining N) such as
0.1 min(p,1-p) = sqrt( p(1-p)/N ).
On the other hand, you argument is flawed because you are not looking
at the sampling properties of your overall procedure. Without trying
to match exactly what you are saying, you are taking something with a
fixed sample size, in which the probability of "YES" is say 75%, and
replacing it with something where you keep on sampling until you
achieve "YES", and thus the probability of arriving at "YES" is 100%.
David Jones
.
.
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