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Re: st: Bootstrapping Conf Intervals - what do they mean?


From   "Dan Weitzenfeld" <dan.weitzenfeld@emsense.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Bootstrapping Conf Intervals - what do they mean?
Date   Wed, 4 Jun 2008 18:09:18 -0700

Thanks all for your help and feedback.  Somehow, I managed to get
through Advanced Statistical Methods as an undergrad totally unaware
of the difference between Bayesian and Frequentist points of view.
I'm definitely going to do the suggested reading.

On Tue, Jun 3, 2008 at 10:08 PM, Clive Nicholas
<clivelists@googlemail.com> wrote:
> Alan Neustadtl replied to Dan Weitzenfeld:
>
>> This is an interesting issue.  Blalock  (Social Statistics 1960, p.
>> 210) provides the following discussion about confidence intervals:
>> "Several words of caution are necessary in interpreting confidence
>> intervals.  The beginning student is likely to use vague phrases such
>> as, "I am 95 per cent confident that the interval contains the
>> parameter", or "the probability is .95 that the parameter is in the
>> interval."  In so doing one may not clearly recognize that the
>> parameter is a fixed value and that it is the intervals that vary from
>> sample to sample.  According to our definition of probability, the
>> probability of the parameter being in any given interval is either
>> zero or one since the parameter is or is not within the specific
>> interval obtained.  ...one's faith is in the procedure used rather
>> than any particular interval.  We can say that the procedure is such
>> that in the long run 95 per cent of the intervals obtained will
>> include the true (fixed) parameter."
>
> [...]
>
> It might be worth pointing out that Iversen (1984) - amongst many
> others - has argued, repeatedly in this case, that using the
> terminology of probability when estimating and interpreting confidence
> intervals is only possible after the generation of Bayesian
> statistical models. Indeed, he also argues that they are
> computationally equivalent yet conceptually different: the 0.95
> statistic is founded as a measure of uncertainty about the point
> estimate; the 95% statistic is seen as a "long-run relative frequency"
> (p38). Confusingly, he mentions the word 'probability' for both
> classical and Bayesian approaches here, but he gives a even clearer
> definition between the two on p31.
>
> Wood (2005) produced a rather nice primer on bootstrapping CIs that
> may be of assistance here, and it should be freely available on the
> Interweb.
>
> --
> Clive Nicholas
>
> [Please DO NOT mail me personally here, but at
> <clivenicholas@hotmail.com>. Thanks!]
>
> Iversen GR (1984) "Bayesian Statistical Inference", Sage University
> Paper on the QASS 07-043, Thousand Oaks: Sage.
>
> Wood M (2005) "Bootstrapped Confidence Intervals as an Approach to
> Statistical Inference", O rganizational Research Methods 8(4): 454-70.
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