Somewhat implicit in how you introduced likelihoods is that the choice of distribution matters, thus the likelihood (and consequently Fischer information) of a parameter is also given the choice of model. I think the binomial distribution is an excellent choice for this video for pedagogical reasons.
@galenseilis5971
3 жыл бұрын
This comment goes beyond the original scope of the video, but it is related. Using the binomial distribution to calculate the likelihood of observing certain combinations of significant/non-significant results of hypothesis tests assumes that the hypothesis tests (even under the null hypothesis) are independent from each other. This is a useful approximation in practice, but isn't necessarily accurate for all combinations of hypothesis tests. If someone knows some general theorems on this topic, I'd love to hear about them. Otherwise, you can do Monte Carlo methods to check if two tests are independent under the null hypothesis.
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