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

 From "Dan Weitzenfeld" 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
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
> 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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```