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If you want your science to be about the real world and not about some hypothetical scenarios that don't exist you have no choice but to do the transposition. E
by BenoitEssiambre 9y ago
If you want your science to be about the real world and not about some hypothetical scenarios that don't exist you have no choice but to do the transposition. Experiments are useless otherwise. There is a reason humans naturally and instinctively do it when they talk about experiments. This is how you describe things in real world human language.
Sure there are debates about priors. These are unavoidable. The hidden assumption in my example is a 50/50 prior on too noisy, not too noisy hypotheses. IMO a reasonable uniform (maximum entropy) prior to start a discussion from. Of course, one should be more precise when doing this type of analysis in a paper. The reason a good prior is hard to define here is not because you shouldn't do the flip, it is because the question that the t-test is trying to answer doesn't make much sense.
- nonbel 9y ago>"If you want your science to be about the real world and not about some hypothetical scenarios that don't exist you have no choice but to do the transposition." How can saying false things make your science "about the the real world"? The only thing I can think of is that by "real world" you are referring to using the publication of massive amounts of incorrect/questionable information as a metric for success. Yes, that is indeed the sham going on. >"There is a reason humans naturally and instinctively do it when they talk about experiments. This is how you describe things in real world human language." I have no problem talking about data without transposing the conditional, if you do that is some issue with your training. >"Sure there are debates about priors." The error you advocate (of transposing the conditional) has nothing to do with priors.
- BenoitEssiambre 9y agoThere is no point in talking about the data if it doesn't tell you useful things about the population or type of thing you are studying, if it's not for building a predictive model of the subjects. This is the entire reason for research. Also P(A|B) = P(B|A) if the prior probabilities are equal, often a reasonable prior.
- nonbel 9y ago>"There is no point in talking about the data if it doesn't tell you useful things about the population or type of thing you are studying" Ok, but I fail to see the relevance of this to anything. >"Also P(A|B) = P(B|A) if the prior probabilities are equal, often a reasonable prior." Here, A = Hypothesis and B = data (or vice versa). You are claiming that the "probability of seeing your data whether or not the hypothesis is correct", is often near the "probability the hypothesis is correct independent of your data"? Based on what? What principle leads you to think these two probabilities should be near each other? BTW, if you actually have one this is like the holy grail of statistics.
- Bromskloss 9y ago> You are claiming that the "probability of seeing your data whether or not the hypothesis is correct", is often near the "probability the hypothesis is correct independent of your data"? Shouldn't that be "the probability of seeing the data, _given_ that the hypothesis is correct" and "the probability of the hypothesis being correct, _given_ that the data has been observed"?
- nonbel 9y agoNo, the other poster is referring to Bayes' rule P(A|B) = P(A)*P(B|A)/P(B). The claim is that it is reasonable to assume P(A) ~ P(B), so that P(A|B) ~ P(B|A). I am referring to P(A) and P(B) in the equation.
- Bromskloss 9y agoAh, OK, got it.
- nonbel 9y agoIts hard to tell over the internet, but if you are being sarcastic please let me know. I have no problem with clarifying further.