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What is the clearest way to state that a 95% CI has a lower bound of A and an upper bound of B.

Most commonly, I see:

$$95\%\textrm{CI}=[A,B]$$

But this seems to imply that the CI is a vector of length two. If I were speaking very precisely, I would say that the 95%CI ranges from A to B.

Perhaps there is a more precise notation, for example:

$$95\%\textrm{CI}\in[A,B]$$

?

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    $\mathbb{P}(X \in [A,B]) = 0.95$2012-05-22
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    You want to be careful about what your probability is with respect to, though. You're often estimating some parameter $\theta$, so it is correct to say $\mathbb{P}(\theta \in [A,B]) = 0.95$ if the probability is with respect to the construction of the interval and not the particular interval constructed, as the probability that $\theta$ is in that fixed interval is $0$ or $1$.2012-05-22
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    @JohnEngbers If I understand correctly - it would be more clear to state that $\mathbb{P}(X|\textrm{model,data} \in [A,B]) = 0.95$? If so, would it be common that this conditioning is implied by context, e.g. in the preceeding text?2012-05-22
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    @Abe : I don't think your proposal is clearer than anything else. In particular, you haven't said what $X$ is! It seems to be something to which you're assigning a probability, so it's an event. What event do you intend it to be. And what can it possibly mean to say that the model and the date are in an particular interval? What you propose as "more clear" is clearly wrong even though it's completely opaque.2012-05-22
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    @MichaelHardy (it is data, not date) I included this information to satisfy the recommendation from JohnEngbers that I provide information about how the interval was constructed. $X$ is any model output parameter (e.g. slope, intercept).2012-05-22
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    @Abe : You're being totally cryptic. Let me hazard another guess as to what you meant: $\mathbb{P}(X\in [A,B] \mid \text{model, data})$.2012-05-22
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    @Abe : ....and no, that's wrong. $\Pr(X\in[A,B]\mid \text{model})$ would be right. Using "$X$" for an unobservable parameter is confusing notation, given the usual conventions.2012-05-22

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