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My question is related to Winstein's explanation of the difference between confidence intervals and credible intervals. Please pardon my (at best) amateur rambling, but this has stumped me thoroughly for the past 5 hours with no realisation in sight!

[Link to Keith Winstein's original post: What's the difference between a confidence interval and a credible interval?

My intuition leads me straight to agreement with Bayesia's solution -- it just seems like the common-sense (and, dare I say, only) way to give a range of jars that'll make sure you have a 70% success rate. (Or am I confusing the two schools here?)

My biggest trouble with the example is how he calculates the confidence intervals by adding up jars (horizontally) from the vertically calculated probabilities. What on earth is going on here?

frequentist estimation

It looks to me as if the table is trying to answer "given that I have Jar B, what range of number-of-chips can I guess that'll get me right coverage 70% of the time?" -- NOT "given that I specify Jars B,C,D as the range, what is the percentage of times that I'll be right about the coverage when it comes to 3-chip cookies?" which is what the example seems to be about.

What am I missing here?

Thanks for your time!

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paxormatic
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1 Answers1

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Your first interpretation "given that I have Jar B, what range of number-of-chips can I guess that'll get me right coverage 70% of the time?" is the good one and the horizontal brackets may be misleading. Nevertheless, once the column-wise "in or out the interval" labeling done (so that it gathers 70% of the data for a given parameter value), the confidence interval for a given observation (the number of chips) consists in a set of jars and this is what represent the horizontal brackets.

peuhp
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  • Excuse the childish framing, but does this make sense: each of the cells in bold effectively says "I am chosen because I land the right number of chips 70% of the time, so if the cookie you pick turns out to be from me, you're good to go (at the same 70% rate)" -- and that's why the horizontal 'addition' is logical? – paxormatic Mar 16 '16 at 14:58
  • @paxormatic Yes if by "70% of the time" you mean "for 70% of the hypothetically drawn cookies whatever their origin". Do not try to simplify too much: the CI is built such as "70% of the CIs contains the parameter value". Hope it helps. – peuhp Mar 17 '16 at 15:18