[https://en.wikipedia.org/wiki/Lindley%27s_paradox](https://en.wikipedia.org/wiki/Lindley%27s_paradox)
In: Mathematics
Ok, this is challenging, I’ll explain the example on the wiki. We want to know if the probability of a newborn being male is 50% or not, we can do this in two ways.
First approach (Bayesian or “a priori”, i.e. before knowing the reality): I assume that the probability is in fact 50%, then I check the official numbers and see how well they fit this this assumption.
Second approach (frequentist or “a posteriori”, i.e. already knowing the real outcome): I take the official numbers and try to find out if they are better explained by one hypothesis or the other.
The point is that the first approach will answer “yes, it’s likely to be 50%” because it will find out that our numbers are a plausible result of that probability; the second approach will answer “no way that it’s exactly 50%” because you can’t make such a precise assumption (and, in our example, if you’re giving such a bold explanation the better one would be that the probability is exactly k/n), it could easily be 51% or 49%.
This is because Bayesian penalizes the “wider” hypothesis (if we say the probability is 50% is a very good hypothesis vs saying that it can be anywhere between 0% and 100%) while frequentist prefers it (it’s infinitely more likely that the percentage is close to 50% than exactly 50%).
Edit: god, this took 40 mins to ely5, I had to sacrifice precision a bit
Latest Answers