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• Thread: 96 Goods vs 59 No Goods

1. Economist
   f405
   

   My friend, not everyone dwells in the asymptotic world. If something is not symmetric about the mean in finite sample, why should pretend N tends to infinity so that our estimator is symmetric about the mean?

   Under regularity conditions, if the parameters have a finite dimension then the Bayesian posteriors asymptotically shrink to the maximum likelihood estimator, and therefore to the parameter of interest. Moreover, any centrality measure of the posterior (conditional mean, or mode) has the same asymptotic distribution as maximum likelihood. In practice, there is absolutely no advantage in one over another, they work the same. Any other statement is just cheap talk of illiterate people.
   However, if the parameters have infinite dimension (a nonparametric curve modeled by sieves), Bayesian estimators can have important failures (inconsistent), there are well known examples, and only in some specific cases the Bayesian nonparametric estimators work well.

   2 years ago # QUOTE 3 Volod 0 Vlad !

2. Economist
   c7b0
   

   You don't need to show Baeysian approaches are equivalent to Frequentists approaches "under" certain assumptions and/or conditions. Why the whole Bayesian ecosystem still appeals to a huge chunk of statisticians until now is that their underlying philosophy begs to differ than frequentiats, even though they admit the lack of practicalities. But they have come up with data-driven fixes recently.

   And the notorious Swan also has converted few days ago.

   2 years ago # QUOTE 1 Volod 0 Vlad !

3. Economist
   16c3
   

   My friend, not everyone dwells in the asymptotic world. If something is not symmetric about the mean in finite sample, why should pretend N tends to infinity so that our estimator is symmetric about the mean?

   Um...that's not how it works. That's not how any of this works.

   2 years ago # QUOTE 0 Volod 5 Vlad !

4. Economist
   f726
   

   Under regularity conditions, if the parameters have a finite dimension then the Bayesian posteriors asymptotically shrink to the maximum likelihood estimator, and therefore to the parameter of interest. Moreover, any centrality measure of the posterior (conditional mean, or mode) has the same asymptotic distribution as maximum likelihood. In practice, there is absolutely no advantage in one over another, they work the same. Any other statement is just cheap talk of illiterate people.
   However, if the parameters have infinite dimension (a nonparametric curve modeled by sieves), Bayesian estimators can have important failures (inconsistent), there are well known examples, and only in some specific cases the Bayesian nonparametric estimators work well.

   XC is that you?

   2 years ago # QUOTE 0 Volod 0 Vlad !

5. Economist
   6e4e
   

   You don't need to show Baeysian approaches are equivalent to Frequentists approaches "under" certain assumptions and/or conditions. Why the whole Bayesian ecosystem still appeals to a huge chunk of statisticians until now is that their underlying philosophy begs to differ than frequentiats, even though they admit the lack of practicalities. But they have come up with data-driven fixes recently.

   And the notorious Swan also has converted few days ago.

   You are just buoyant on a space filled with speckles, without knowing nowhere to head to, hoping to garner one more data, one more data,..., one more.

   2 years ago # QUOTE 0 Volod 0 Vlad !

6. Economist
   d2a9
   

   Under regularity conditions, if the parameters have a finite dimension then the Bayesian posteriors asymptotically shrink to the maximum likelihood estimator, and therefore to the parameter of interest. Moreover, any centrality measure of the posterior (conditional mean, or mode) has the same asymptotic distribution as maximum likelihood. In practice, there is absolutely no advantage in one over another, they work the same. Any other statement is just cheap talk of illiterate people.

   While your comment is correct, Bayesian and frequentist statistics start from very different initial assumptions. With Bayesian methods, you have to have some sort of prior, even if it's an agnostic "flat" prior. And with frequentist methods, you have to implicitly you assume that your sample was generated by a process that could (at least theoretically) repeated infinitely many times. Depending on the circumstances, one assumption may be stronger than the other.

   2 years ago # QUOTE 0 Volod 0 Vlad !

7. Economist
   3ba6
   

   Under regularity conditions, if the parameters have a finite dimension then the Bayesian posteriors asymptotically shrink to the maximum likelihood estimator, and therefore to the parameter of interest. Moreover, any centrality measure of the posterior (conditional mean, or mode) has the same asymptotic distribution as maximum likelihood. In practice, there is absolutely no advantage in one over another, they work the same. Any other statement is just cheap talk of illiterate people.

   While your comment is correct, Bayesian and frequentist statistics start from very different initial assumptions. With Bayesian methods, you have to have some sort of prior, even if it's an agnostic "flat" prior. And with frequentist methods, you have to implicitly you assume that your sample was generated by a process that could (at least theoretically) repeated infinitely many times. Depending on the circumstances, one assumption may be stronger than the other.

   My comment is correct, both conceptually and formally. The prior is absolutely irrelevant for the outcome, provided it is supported on a set that contains the true parameter as an interior point. If the support has infinite are (Lesgue measure if you prefer), that excludes the possibility of a flat prior covering all possible values for the parameter, so you cannot really be non-informative as the true parameter can be anywhere. That is a limitation of Bayes. If you take a non-flat prior, that is not a problem. But if this prior is concentrated far away from the true parameter, with finite samples the posterior might be concentrated far away from the parameter (asymptotically, it is converging anyway, but this might require a very large sample size if the prior concentrates its mass in the wrong area)

   2 years ago # QUOTE 0 Volod 2 Vlad !

8. Economist
   3ba6
   

   And certainly, Bayesian is not about assuming "random parameters" and learning about them. It is completely irrelevant how nature generated the parameter, but once it is set all observations came from the same parameter, this is the parameter that both Maximum Likelihod and Bayes method estimate, and the key properties of both estimators are asymptotic. Large N, little else matters.

   2 years ago # QUOTE 0 Volod 0 Vlad !

9. Economist
   d2a9
   

   My comment is correct, both conceptually and formally. The prior is absolutely irrelevant for the outcome, provided it is supported on a set that contains the true parameter as an interior point.

   Irrelevant if N → ∞

   2 years ago # QUOTE 0 Volod 0 Vlad !

10. Economist
    1c0e
    

    My friend, not everyone dwells in the asymptotic world. If something is not symmetric about the mean in finite sample, why should pretend N tends to infinity so that our estimator is symmetric about the mean?

    Bayesians don't understand probability, according to Kolmogorov:

    "The epistemological value of the theory of probability is revealed only by limit theorems."

    2 years ago # QUOTE 1 Volod 0 Vlad !

11. Economist
    3714
    

    Actually used in tech. But all the good papers in this space are internal. So academia only knows the bad leftovers.

    2 years ago # QUOTE 0 Volod 0 Vlad !

12. Economist
    c3ea
    

    it's a tool. use it if/when needed. full stop.

    2 years ago # QUOTE 0 Volod 0 Vlad !

13. Economist
    d2a9
    

    And certainly, Bayesian is not about assuming "random parameters" and learning about them. It is completely irrelevant how nature generated the parameter, but once it is set all observations came from the same parameter, this is the parameter that both Maximum Likelihod and Bayes method estimate, and the key properties of both estimators are asymptotic. Large N, little else matters.

    Just out of curiosity: which Bayesian textbook gives a good discussion of asymptotics?

    2 years ago # QUOTE 0 Volod 0 Vlad !

14. Economist
    3ba6
    

    And certainly, Bayesian is not about assuming "random parameters" and learning about them. It is completely irrelevant how nature generated the parameter, but once it is set all observations came from the same parameter, this is the parameter that both Maximum Likelihod and Bayes method estimate, and the key properties of both estimators are asymptotic. Large N, little else matters.

    Just out of curiosity: which Bayesian textbook gives a good discussion of asymptotics?

    Most Bayesians usually do not discuss these topics well, but this is sometimes discussed by "frequentists". A good reference is van der Vaart (1998), "asymptotic statistics". This is a bit technical. You can find a simplified discussion in Esteban-Bravo and Vidal-Sanz (2021) "Marketing Research Methods: Quantitative and Qualitative Approaches".

    2 years ago # QUOTE 1 Volod 0 Vlad !

15. Economist
    3ba6
    

    For nonparametric Bayesian statistics see van der Vaart (2017) "Fundamentals of Nonparametric Bayesian Inference"

    2 years ago # QUOTE 0 Volod 0 Vlad !

16. Economist
    3ba6
    

    Here there are some sketchy ideas about consistency of Bayes estimators in parametric context: http://www.math.leidenuniv.nl/~avdvaart/talks/ICM.pdf

    2 years ago # QUOTE 0 Volod 0 Vlad !

17. Economist
    9935
    

    http://www.stat.columbia.edu/~gelman/research/published/philosophy.pdf

    a bayesian and a non-bayesian write a paper on bayesian philosophy

    2 years ago # QUOTE 0 Volod 0 Vlad !

18. Economist
    9cee
    

    Under regularity conditions, if the parameters have a finite dimension then the Bayesian posteriors asymptotically shrink to the maximum likelihood estimator, and therefore to the parameter of interest. Moreover, any centrality measure of the posterior (conditional mean, or mode) has the same asymptotic distribution as maximum likelihood. In practice, there is absolutely no advantage in one over another, they work the same. Any other statement is just cheap talk of illiterate people.
    However, if the parameters have infinite dimension (a nonparametric curve modeled by sieves), Bayesian estimators can have important failures (inconsistent), there are well known examples, and only in some specific cases the Bayesian nonparametric estimators work well.

    what about for small samples?

    2 years ago # QUOTE 0 Volod 0 Vlad !

19. Economist
    3ba6
    

    Under regularity conditions, if the parameters have a finite dimension then the Bayesian posteriors asymptotically shrink to the maximum likelihood estimator, and therefore to the parameter of interest. Moreover, any centrality measure of the posterior (conditional mean, or mode) has the same asymptotic distribution as maximum likelihood. In practice, there is absolutely no advantage in one over another, they work the same. Any other statement is just cheap talk of illiterate people.
    However, if the parameters have infinite dimension (a nonparametric curve modeled by sieves), Bayesian estimators can have important failures (inconsistent), there are well known examples, and only in some specific cases the Bayesian nonparametric estimators work well.

    what about for small samples?

    In small samples Bayesian methods can be terrible, because all depends on the prior. Sometimes they can be great if you are lucky, but you do not know in general. But to be honest, the same happens with maximum likelihood when N small and the function is highly nonlinear, depending on the starting point of the algorithm it can get a bad local maxima, and you cannot use good robust optimization methods if the number of parameters is large (incidentally, large dimensions also are expensive when Bayesians need to compute their integrals with Montecarlo). So, we need always large samples compared to the number of parameters. Otherwise, stick to basics (means, variances,...)

    2 years ago # QUOTE 0 Volod 3 Vlad !

20. Economist
    3ba6
    

    Bayesian claims are oftenpropaganda, they are neither better nor worse in general than maximum likelihood. For example, in VAR models it is often claim that Bayesian methods works better, but not really; see:

    https://ideas.repec.org/p/bge/wpaper/776.html

    2 years ago # QUOTE 1 Volod 2 Vlad !

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