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Every time I see an article like this, I eagerly read it hoping to find a cogent and coherent criticism of Bayesian stats, and it always ends up being a straw m

Every time I see an article like this, I eagerly read it hoping to find a cogent and coherent criticism of Bayesian stats, and it always ends up being a straw man or a very fair critique of somebody not correctly applying or interpreting an application of Bayes’ theorem. Bayesian stats is nothing more than a rigorous way to transform beliefs + data into a posterior. Yes, flat priors are not always the best choice. That’s not a criticism of Bayesian stats. It’s a statement about how actually formulating a prior is often times the hardest part of a problem. Is Bayesian stats useful for describing or understanding QM? Idk, again, not really it’s job... Use Bayesian stats, not with an air of suspicion, but a respect for the fact that it will give you the results implied by your data and prior, under your model assumptions. Nothing more, nothing less. By the way, what is the alternative if you find yourself in a situation where your result depends strongly on your prior and you aren’t really sure how to choose your prior? Wave your hands and find an ad hoc frequentist approach? How about just admitting to yourself that your data isn’t enough to make up for the fact that you can’t really quantify your true prior belief? If you read this and disagree, I sincerely implore you to comment — I just don’t understand the “debate” aspect of Bayesian stats. Some people misunderstand what Bayesian stats is sometimes (very understandable) but I have yet to see a legitimate philosophical or mathematical critique of the Bayesian approach that really made any sense to me. I would like to know if I am wrong though...

jedbrown 7y ago
> it always ends up being a straw man or a very fair critique of somebody not correctly applying or interpreting an application of Bayes’ theorem. I can't tell from your comment if you're aware that Andrew is the first author of the leading textbook on Bayesian methods. http://www.stat.columbia.edu/~gelman/book/ http://www.stat.columbia.edu/~gelman/book/
- astrophysician 7y ago
  That’s awesome, and maybe I misunderstand his argument (very possible, in fact my main reason for posting this comment). Am I not understanding the arguments being made here? I have not been following these developments regarding using Bayesian stats in QM, it’s just that if Bayesian stats doesn’t help us understand QM it doesn’t mean there’s a “hole” because Bayesian stats makes no claim whatsoever that it has any applicability to QM. Am I just not understanding?
  - bjornsing 7y ago
    I very much agree. It’s well known that probability theory is insufficient to explain the evolution of a QM system (i.e. the Schrödinger equation cannot be expressed in terms of probability). This is an interesting fact about QM, but in no way constitutes a hole in probability theory or Bayesian statistics.
steerablesafe 7y ago
> That’s not a criticism of Bayesian stats. It’s a statement about how actually formulating a prior is often times the hardest part of a problem. Bayesian statatistics doesn't give a satisfying answer/method for choosing priors. Choosing priors is part of statistics. Therefore Bayesian statistics has a "hole" in it.
- astrophysician 7y ago
  > Bayesian statistics doesn’t give a satisfying answer/method for choosing priors I absolutely agree with you. Priors are the (very difficult) job of the practitioner. > choosing priors is a part of statistics Ah so I think I agree, maybe would nitpick and say priors are part of statistics and CHOOSING priors is part of modeling maybe? Not totally comfortable with that characterization either it’s just that “priors” and “choosing priors” are two different things. > therefore Bayesian statistics has a “hole” in it. Completely disagree; this is my main understanding of the argument against Bayesian statistics, I just don’t understand how this follows from the last statement. Priors are hard. But they are explicit! And a necessary ingredient of the posterior. It’s not like we can say “oh priors are hard, so let’s not do Bayesian stats but instead let’s do X” what is X?
- 08-15 7y ago
  E. T. Jaynes gave some very good answers (symmetry groups and maximum entropy principle). You should read "Probability Theory: The Logic Of Science". In it, you will learn that the supposed "hole" has been closed pretty nicely.
  - bjornsing 7y ago
    My favorite book of all time. :)
- bjornsing 7y ago
  Or you could say that the interpretation of data is fundamentally and unavoidably subjective.
astrophysician 7y ago
Replying since it's been too long to edit: Now that I've taken some time to actually READ the article referenced in this post, I have a couple more things to say; basically: I agree with virtually everything that they're saying in the paper (except that I still don't understand why Bayesian stats failing in QM says absolutely anything about the validity of Bayesian stats), and I think I set up my own straw man here a bit. I thought this was another "Bayesian stats is bad because priors" post, which in a way it SORT of is, but their arguments are a bit more on the side of "you should take 'Bayesian' analyses with a large grain of salt sometimes because...well...priors" <- and THAT I completely agree with. The only beef I have with these types of articles are when they seem to imply that because priors sometimes have an outsized effect on the results, we should not use Bayesian statistics/analyses. But really, there is no other option. If you have a statistical question, you're stuck with having to answer for your priors. That being said, what IS good advice is to not simply believe every 'Bayesian' conclusion for exactly that reason -- that result is only as good as the (1) prior, (2) model assumptions, and (3) the data. (2) and (3) are easy to fight about, but (1) can be hard to evaluate, and easily can lead all of us astray even when the prior sounds reasonable (flat priors).

jedbrown 7y ago

> it always ends up being a straw man or a very fair critique of somebody not correctly applying or interpreting an application of Bayes’ theorem. I can't tell from your comment if you're aware that Andrew is the first author of the leading textbook on Bayesian methods. http://www.stat.columbia.edu/~gelman/book/ http://www.stat.columbia.edu/~gelman/book/

astrophysician 7y ago
That’s awesome, and maybe I misunderstand his argument (very possible, in fact my main reason for posting this comment). Am I not understanding the arguments being made here? I have not been following these developments regarding using Bayesian stats in QM, it’s just that if Bayesian stats doesn’t help us understand QM it doesn’t mean there’s a “hole” because Bayesian stats makes no claim whatsoever that it has any applicability to QM. Am I just not understanding?
- bjornsing 7y ago
  I very much agree. It’s well known that probability theory is insufficient to explain the evolution of a QM system (i.e. the Schrödinger equation cannot be expressed in terms of probability). This is an interesting fact about QM, but in no way constitutes a hole in probability theory or Bayesian statistics.

steerablesafe 7y ago

> That’s not a criticism of Bayesian stats. It’s a statement about how actually formulating a prior is often times the hardest part of a problem. Bayesian statatistics doesn't give a satisfying answer/method for choosing priors. Choosing priors is part of statistics. Therefore Bayesian statistics has a "hole" in it.

astrophysician 7y ago
> Bayesian statistics doesn’t give a satisfying answer/method for choosing priors I absolutely agree with you. Priors are the (very difficult) job of the practitioner. > choosing priors is a part of statistics Ah so I think I agree, maybe would nitpick and say priors are part of statistics and CHOOSING priors is part of modeling maybe? Not totally comfortable with that characterization either it’s just that “priors” and “choosing priors” are two different things. > therefore Bayesian statistics has a “hole” in it. Completely disagree; this is my main understanding of the argument against Bayesian statistics, I just don’t understand how this follows from the last statement. Priors are hard. But they are explicit! And a necessary ingredient of the posterior. It’s not like we can say “oh priors are hard, so let’s not do Bayesian stats but instead let’s do X” what is X?
08-15 7y ago
E. T. Jaynes gave some very good answers (symmetry groups and maximum entropy principle). You should read "Probability Theory: The Logic Of Science". In it, you will learn that the supposed "hole" has been closed pretty nicely.
- bjornsing 7y ago
  My favorite book of all time. :)
bjornsing 7y ago
Or you could say that the interpretation of data is fundamentally and unavoidably subjective.

astrophysician 7y ago

Replying since it's been too long to edit: Now that I've taken some time to actually READ the article referenced in this post, I have a couple more things to say; basically: I agree with virtually everything that they're saying in the paper (except that I still don't understand why Bayesian stats failing in QM says absolutely anything about the validity of Bayesian stats), and I think I set up my own straw man here a bit. I thought this was another "Bayesian stats is bad because priors" post, which in a way it SORT of is, but their arguments are a bit more on the side of "you should take 'Bayesian' analyses with a large grain of salt sometimes because...well...priors" <- and THAT I completely agree with. The only beef I have with these types of articles are when they seem to imply that because priors sometimes have an outsized effect on the results, we should not use Bayesian statistics/analyses. But really, there is no other option. If you have a statistical question, you're stuck with having to answer for your priors. That being said, what IS good advice is to not simply believe every 'Bayesian' conclusion for exactly that reason -- that result is only as good as the (1) prior, (2) model assumptions, and (3) the data. (2) and (3) are easy to fight about, but (1) can be hard to evaluate, and easily can lead all of us astray even when the prior sounds reasonable (flat priors).