0

Suppose I have a population of interest, let's say P1, I obtain data through a sample, D1 and obtain a 95% confidence interval on a parameter value of interest, CI1. The interpretation of the probability is clear - it is the long run frequency of the confidence interval covering the true parameter value if the sampling was repeated on P1. So suppose I run this same sampling technique on P1, and obtain another 95% confidence interval, and this is done and infinite amount of time, and then I would get 95% of the confidence intervals covering the true parameter value in P1.

But now suppose instead I have another distinct population of interest, P2, and again, through the same process as above, obtain D2, and construct a 95% confidence interval, CI2.

I repeat this an infinite amount of times on seperate population of interest, P3, P4, ... My understanding is that 95% of these confidence intervals, CI1, CI2, .... will each cover their own (distinct) true parameter value.

Then, what now is the, frequentist interpretation of probability, given that the population of interest is not fixed, but some sort of cartesian product of distinct populations? How is the frequentist interpretation applied here?

shem
  • 144
  • You describe correctly how frequentist confidence intervals are defined. It is not clear where do you see a problem – J. Delaney May 03 '22 at 10:53
  • Apologies, my issue is: how is this new probability defined, given that now our population/experiment is no longer fixed to one population/experiment, but differs for each. (This probability exists since the 95% applies even across these various confidence intervals constructed) – shem May 03 '22 at 11:05
  • The coverage probability is defined separately for each experiment. It makes no difference if you consider other experiments. – J. Delaney May 03 '22 at 11:57

0 Answers0