How "be nice" policies bring us to the tyranny of nonsense.
Monday, September 5, 2016
Injustice in the CI fallacy
Here I have posted a question asking how can you tell that the probability of true value in the confidence interval is nonsense, yet, it is legal to speak about credibility interval when it serves the same purpose? They shut down my question with excuse that they say what I say they say. Yes, they give me back the link that I gave them, without pointing out how can this answer my question. It is notable that they confess that site-owning judges do not bother to read your posts. All they need to make sanctions against you is to skip through the post, find the familiar words and fire well-prepared answer in advance. They think that FAQ means that everybody asks the same question all over again and you do not need to try to understand it. Just post the link to the answer you have last time to the question with these keywords.
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?
put on hold as primarily opinion-based by whuber♦2 days ago
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