# Confidence intervals fallacy once again [on hold]

I see that all the answers to what is the fallacy respond (e.g here and here to name some) that we know that the parameter is within CI or not for sure and therefore, unlike Bayesian credibility interval, it is technically illegal to speak about probability of certain event. As you know, I have acute feeling of injustice. Why can you say that Bayesian credibility contains the value with certainty 95% but cannot say the same in case of CI? You say that you know for sure. So, why don't you apply the same logic to Bayesian interval, why do you keep the credibility 95% despite you say that it is illegal to speak about probability once your knowledge is 100%?
Reading the baesian paper on the subject, I see that it gives the same doubtful reasoning in the beginning. But, looking deeper, they demonstrate that there are many procedures that give different 50% CIs. Not only the CIs contradict to each other, they are opposite to common sense and only (bayesian) likelihood gives meaningful interval. That is, the demo goal is to locate a center of submarine that produces two random bubbles along its length of 10 meters. All CIs agree that the larger the distance between the bubbles, the less certain we are about the sought center. If two bubbles come from a single point then the center is there. Meantime, exactly opposite is true: when bubbles happen to come from opposite ends of the submarine, we know it location and location of its center for sure and have maximal ±5m uncertainty when bubbles are emitted at the same location. In the long run, article says, CIs should give 50% matches about the su center found in them but in particular situations, without knowing exact location of the center (that is why Bayesian credibility can be true), we can be absolute sure that sought center is within or outside the CI, which makes the 50% confidence meaningless and misleading.
Now, I wonder why do all the answers insist on double standards instead of giving this, in-depth, story. Don't people just dislike justice or I am missing something, how double standards follow from detailed analysis?
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## put on hold as primarily opinion-based by whuber♦2 days ago

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.If this question can be reworded to fit the rules in the help center, please edit your question.
"illegal" doesn't mean what you seem to think it means. – EnergyNumbers 2 days ago
@EnergyNumbers This is what my post is against: the nebulousness. I ask to remove it. It is clear from my post that they argue against there is n% probability that your value is within CI. I use word illegal equivalently with the traditional argument why you cannot do that. I want you to be more clear on why it is illegal. – Little Alien 2 days ago
I don't see how the vague, general questions "don't people dislike justice" or "how [can] double standards follow from detailed analysis" can be answered in this forum. Skimming the preceding text suggests you might want to read about differences between confidence and credible intervals. If that doesn't address your concerns, then please edit this post to include a clear, specific, objectively answerable question. – whuber 2 days ago