On 22 Nov 2003 09:46:20 -0800, [EMAIL PROTECTED] (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.
What you describe, below, is *not* an iteration to get a confidence interval. You describe iterating to get a *point-estimate*. > > So you iterate ad infinitum. As you go, the p goes down, and the > interval gets wider. How unlikely is it to flip 20 heads in a row? I can get an estimate as you describe it, by flipping a coin (or having a computer fake it) about a million times. > 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. Where is the *interval*? Whose interval? What interval? I get an estimate that it takes about a million flips to get that event, "20 in a row"; so I conclude that the p is about 1 in a million. Is the time-to-first occurrence a good estimate of the p? Sometimes it is. I should be able to compute a better estimate if I let the computer keep flipping until it has found dozens or hundreds of the event. One per million, using n, is a "point estimate." I have to repeat that experiment -- of flipping a million coins -- 500 times or more in order to generate a confidence interval (with any confidence as to the accuracy of its size). > > 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. I hope this clarifies how you were oversimplifying things. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html "Taxes are the price we pay for civilization." . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
