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Re: st: Bootstrapping question


From   Austin Nichols <austinnichols@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Bootstrapping question
Date   Fri, 8 Feb 2013 10:02:45 -0500

Henry Ilian <Henry.Ilian@dfa.state.ny.us> :
See also section 7.4.2 in
http://www.albany.edu/physics/ACaticha-EIFP-book.pdf
for why inference for a multinomial probability minimizes distance on
the surface of a hypersphere.

On Fri, Feb 8, 2013 at 9:49 AM, Austin Nichols <austinnichols@gmail.com> wrote:
> Bootstrapping is designed to improve CIs by making their coverage
> better, not by making them smaller! A better approach for your case
> would be Bayesian, but again a better CI does not necessarily mean a
> smaller CI. Some priors might result in smaller credible intervals,
> but others in larger, and you need to describe the dependence of your
> results on your assumptions. If you estimate 15 ways and only report
> the one that accords with the conclusion you want, you are committing
> scientific fraud.
>
> For the multinomial case, a flat prior is not the face of a simplex:
> see also section 5.2 in http://www.tilman-neumann.de/docs/BIEP.pdf
>
> Depending on how serious you are about getting the smallest possible
> CI, you may need to do a lot of reading about maximum entropy methods.
>
> On Thursday, February 7, 2013, Ilian, Henry (ACS) wrote:
> Nick, you're right. Some of the potential (and actual) outcomes have
> observed zeros. I looked everywhere I could think of for the formula
> to compute sample sizes for multiple categories but couldn't find it.
> In the process, I read somewhere that the problem of multiple
> categories reduces to a two-category problem. I asked one statistician
> about this, and he said not true and suggested I take his on-line
> advanced sampling class. I certainly am considering that, but for the
> meanwhile, I still have a sample size that results in very wide
> confidence intervals. Again, my understanding from reading about
> bootstrapping is that one of the things bootstrapping was designed to
> do was to improve estimates of confidence intervals in small samples.
> My question is, can I use it in this situation, and if I do, what do I
> report?
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