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In Tom Mitchell's 1997 Machine Learning, a confidence interval is defined on page 138 as

An N% confidence interval for some parameter p is an interval that is expected with probability N% to contain p.

However, from questions as Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?, it seems as if this is precisely not the case.

Is Tom Mitchell mistaken?

user217047
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  • you really don't want to go into this debate – rep_ho Aug 08 '18 at 14:09
  • @rep_ho - as an engineer (non-statistician) that has to relate this stuff to business people (mathematically and technically illiterate) I'm really quite curious about the answer here. This is math, not lawers, so this is about definition and logic, not semantics. There are 3 allowed answers. 1) tom is right, this is wrong because of definition + irrefutable logic, 2) this is right, tom is wrong because of definition + irrefutable, or 3) they are both right because of unifying logical statement "x" and previous content. Why the "debate"? – EngrStudent Aug 08 '18 at 14:13
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    I don't know the book, but if this is indeed his definition of a [tag:confidence-interval], then yes indeed, he is mistaken as per the linked thread. See especially [John's answer](https://stats.stackexchange.com/a/26453/1352). I don't see much else to do here than to vote to close as a duplicate. – Stephan Kolassa Aug 08 '18 at 15:04
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    I'll stick my neck out here: [Mitchell is a computer scientist](http://www.cs.cmu.edu/~tom/). CIs are a statistical concept. I trust computer scientists to define statistical concepts about as much as I trust statisticians to define computer science concepts. Make of that what you will. (*Me?* I'm a mathematician. I just play a statistician on CV. Ask me about domains of holomorphy.) – Stephan Kolassa Aug 08 '18 at 15:07
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    To provide the complement to @StephanKolassa's comments, it's possible he's a [Bayesian](https://en.wikipedia.org/wiki/Bayesian_probability) & this is essentially a typo--he meant [*credible* interval](https://en.wikipedia.org/wiki/Credible_interval). – gung - Reinstate Monica Aug 08 '18 at 15:38
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    @EngrStudent it is true, that if you were to bet on a 95% CI to contain the mean with 1/20 course, you are expected not to lose or win any money. This avoids the whole philosophical debate and it's understandable for business people as well. – rep_ho Aug 09 '18 at 10:04

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