Timeline for Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
Current License: CC BY-SA 4.0
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| Apr 15, 2024 at 21:59 | comment | added | jginestet | ...cont... The true statement should have been "the datasets (39,39) and (40,40) provide 50% CI's, while the datasets (39,40) and (40,39) provide 100% CI's". No counter-example anymore. The first statement does not use the information to him when he makes the 2nd. And my proposed statement can be made BEFORE the data is collected, knowing the model. His example may be viewed as a Texas sharpshooter fallacy (using information -where the bullets landed- not available to another shooter) | |
| Apr 15, 2024 at 21:56 | comment | added | jginestet | @GeoffreyJohnson, Dikran's example is a false counter-example. The statement "the datasets (39,39), (39,40), (40,39), and (40,40) provide 75% confidence intervals" does not make use of the full informatiuon we have about the probability model (how our random process works). But the statement (39,39) is only a 50% CI does. Apples and oranges. There is NO contradicton here. ...cont... | |
| Dec 23, 2021 at 23:10 | comment | added | Dikran Marsupial | "We can therefore construct the 100% confidence interval θ∈(28,29). This is a direct contradiction to Dikran's claim..." my answer started "...the frequentist definition of a probability doesn't allow a nontrivial probability to be applied to the outcome of a particular experiment...". A 100% confidence interval is an example of assigning a trivial probability (i.e. 0 or 1) to a particular outcome, so that does not contradict what I said. | |
| Dec 23, 2021 at 23:01 | comment | added | Dikran Marsupial | "The 100% credible interval is (28,29), " fine, give me a 75% confidence interval that contains the true value with probability 75%. | |
| Dec 23, 2021 at 22:57 | comment | added | Dikran Marsupial | BTW you appear to have two non-overlapping 75% confidence intervals. There cannot be a 75% probability of the true value being in both of them as probabilities of exclusive events can't sum to more than one. | |
| Dec 23, 2021 at 22:48 | comment | added | Dikran Marsupial | "This statement calls into question the likelihood itself which is at the core of Bayesian inference." I do not see what that is the case. The likelihood is the probability of observing a particular set of observations from a particular model. That is true both of the individual sample of data and of the population of samples under a repeated experiment setting. | |
| Dec 23, 2021 at 22:46 | comment | added | Dikran Marsupial | "One conclusion is to "rule out" H0:θ=28 at the 0.25" as I pointed out on your other answer, this is not stating a probability of the true value being in the interval (because a frequentist cannot assign a non-trivial probability to the truth of a particular proposition). This is not a criticism of frequentist statistics. | |
| Dec 23, 2021 at 22:42 | comment | added | Dikran Marsupial | " Dikran Marsupial claims that since the confidence level of the confidence interval is a statement about repeated experiments it does not allow one to infer the unknown fixed true θ based on a particular sample. " No, I made no such claim. I'm sorry, but if you are going to be insulting (stats.stackexchange.com/questions/2272/…) and then repeatedly misrepresent what I have written, I think the chance of reaching agreement here is fairly slim. | |
| Dec 23, 2021 at 22:40 | comment | added | Dikran Marsupial | "(without reference to a prior) " no, I stated the reasoning for that prior "and we have no reason to suppose that 29 is more likely than 28". | |
| Dec 23, 2021 at 22:38 | comment | added | Dikran Marsupial | "no confidence interval is admissible as a set of plausible parameter values consistent with the observed data:" No, that was not what I said. The example was demonstrating that the probability of the true value being in an X% confidence interval is not X%. It was Jaynes example, not McKay's where we can be sure that the true value is not in a valid confidence interval. | |
| Dec 23, 2021 at 22:31 | comment | added | Geoffrey Johnson | In his answer Dikran also states, "...the frequentist definition of a probability... [applies]... only to some fictitious population of experiments from which this particular experiment can be considered a sample." This statement calls into question the likelihood itself which is at the core of Bayesian inference. If Dikran is adamant about his statement, then he must also dismiss Bayesian inference as well. | |
| Dec 23, 2021 at 22:18 | history | answered | Geoffrey Johnson | CC BY-SA 4.0 |