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What are the advantages of Bayesian statistics over traditional (frequentist) methods?

The link below is really helpful, but the topic still seems controversial and complicated to me. Can someone put it simple?

When are Bayesian methods preferable to Frequentist?

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  • $\begingroup$ This is a really big question, that whole books could be written about. I don't think it's possible to answer it in a forum like this in any kind of satisfactory way. Try making it simpler (just ask one question). $\endgroup$ – Jeremy Miles Nov 25 '19 at 4:12
  • $\begingroup$ thank you very much, Jeremy. I'm trying to understand the main applications of Bayesian statistics to see if it is worth reading whole books about the subject, instead of using frequentist analyses. It's a fascinating topic, I'll try to simplify my question. $\endgroup$ – Fabiano Pinheiro da Silva Nov 25 '19 at 7:22
  • $\begingroup$ I am constantly advertising this course and I hope it is not against this board's policy: BBR course on Stats by Frank Harrell. He provides the comparison starting from lecture 4 in a systematic manner, addressing the problems of Frequentists methods and answering from the Bayesian point of view. $\endgroup$ – German Demidov Nov 25 '19 at 9:59
  • $\begingroup$ There is a short answer: It is worth reading whole books about, even if you then choose to stay with frequentism. The matter is controversial and there will not be easy answers. In order to form your own opinion and make your own choices you will have to read a book or two. $\endgroup$ – Bernhard Nov 25 '19 at 10:12
  • $\begingroup$ I advise to go to youtube and see Andrew Gelmans talk on "Crimes against Data". It's fun and it shows, how many things are done wrong in practical/published statistics. Even if the talk is not primarily about Frequentism/Bayes. If you get the feeling, that following old paths is not the best way to deal with problems and that you should be open to think more about statistics, you may then get a bunch of motivation to read about "new" ways to tackle statistics problems. Then read a good, not to complicated book. $\endgroup$ – Bernhard Nov 25 '19 at 10:18
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Bayesian statistics can be applied to most statistical questions (I won't say all because it's impossible to know, but all the stuff that commonly comes up on the frequentist side can be done in a Bayesian context).

The advantages of Bayesian statistics include the ability to directly sample the distribution of the parameter of interest, and the ability to model complex, intermixed random variables that make up a single system. You can also encode prior information in your models.

The assumptions tend to be stronger than frequentist statistics as a result. You have to have some prior information, which is really another parameter to figure out. You also spend a lot of time figuring out how to sample from intractable distributions (MC, VI).

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Can Bayesian analysis be applied to any type of statistical question?

I think the answer is "yes", but care should be taken. With enough data, the results between bayesian and frequenstist methods start to look very similar (that is, unless you have unreasonably strong priors).

What are the advantages of Bayesian statistics over traditional (frequentist) methods and its main assumptions?

That you can incorporate prior information into your models is a huge advantage. The prior information let's you "hit the ground running" so to speak.

You can create very complex models to model most any phenomenon. I use Bayesian statistics to model drug disposition between patients. This not only lets me understand how a particular patient may metabolize a drug, but also how a new patient (one which I may have not measured yet) may metabolize a drug.

However, Bayesianism is very complex and not something you can just pick up. The processes of model validation is more involved than frequenstist stats.

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