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So, I'm diving into learning statistics. I'm finally starting to intuitively grasp the difference between bayesianism and frequentism.

I understand that both are neither wrong nor right. To further my understanding of the two, my question is:

What are some examples where a frequntist methods are better, and what are some examples where baysian methods are better? (preferably in the context of science)

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    $\begingroup$ "I understand that both are neither wrong nor right." Obviously you are not a Bayesian. $\endgroup$ – Mark L. Stone Sep 23 '15 at 11:04
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Both are completely valid any time you do inference: you try to determine something about the distribution of the data coming at you. Just use what you feel most comfortable with.

If you are trying to act on that information in an automated way though, I'm not sure if you can really do that with frequentist methods (I don't know frequentist methods super well) whereas it's really easy to use the result of a Bayesian inference to guide decisions automatically. For example, if you want to drive a robot, or to buy and sell stocks, etc.

Finally, in rare cases, you know exactly how the data is generated, so that you are sure that the probabilistic model you are using is the correct one. In that case, I think there is a stronger argument for just computing the posterior distribution, because Bayes formula is the "law of the land", but some people would argue that, even then, they want to use frequentist methods. The best argument for frequentist methods in this case is that they (frequentist methods) give guarantees that are valid even in the worst possible case.

In the end, it's best to be familiar with both angles

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