3 ms·

There's always a more complicated model.

zozbot234 3y ago
The "more complicated" version of frequentist statistics is called robust statistics. There's most likely a way to rephrase your favorite Bayesian analysis so as to make it fully kosher from a "robust+frequentist" point of view, even keeping the math unchanged. It just goes to show how silly the "controversy" is.
PheonixPharts 3y ago
Bayesian statistics is fundamentally less complicated than Frequentist statistics since everything can be derived from a very simple set of first principles, rather than complex frameworks of ad hoc testing methodologies.
- ivansavz 3y ago
  > Bayesian statistics is fundamentally less complicated than Frequentist statistics [...] I broadly agree with you, but I'm wondering if you would reconsider your qualification as "less complicated" if you consider beginner learners. E.g. someone who knows basic descriptive statistics and probability theory, and is making first contact with inferential statistics. Specifically, assume a learner who knows what an integral is, but is far from proficient with it (UGRAD student, not a GRAD student). I was reading this paper[1] recently, which highlights two difficulties of teaching Bayesian stats: 1) the mathematical complexity of understanding conditional probability distributions, and 2) the lack of well defined, broadly accepted conventions for what priors to use in specific data analysis scenarios. I think a computational approach to prob theory could mitigate 1), but 2) remains a problem—the freedom to choose priors, is also a burden... [1] https://www.stat.purdue.edu/~dsmoore/articles/BayesPedagogy.pdf https://www.stat.purdue.edu/~dsmoore/articles/BayesPedagogy....
  - ivansavz 3y ago
    For context, I'm not taking sides in the frequentist-vs-Bayesian debate, but coming from a practical problem: I'm working on a INTRO TO STATS book right now, and I would like to include a chapter on Bayesian statistics, but I'm not sure what specific analyses to showcase and recommend as "standard" approaches. Unlike the canonical t-tests and ANOVAs of frequentists, Bayesian statistics doesn't have canonical procedures (that I know of) that I can wholeheartedly recommend as "must know" and ready to use broadly. Maybe someone here might have suggestions? The closest thing that comes to mind is "Bayes factors," which has some traction (usage), but apparently they have lots of problems and limitations too, cf. https://www.youtube.com/watch?v=MqeWpR6S4XA https://www.youtube.com/watch?v=MqeWpR6S4XA
    - maltelau 3y ago
      Maybe you would find it useful to read a textbook on bayesian stats for inspiration. I can recommend Richard McElreath's "Statistical Rethinking" which makes it very clear how inflexible it is to just know recipes like t-tests or anovas. The canonical approach is to build a generative model with a parameter (or multiple for ~anova) that codes for the difference between groups and do inference on that parameter of interest. Most of the recipes taught in statistics classes can be modelled as a regression of some kind (this counts for frequentist stats too, see https://lindeloev.github.io/tests-as-linear/ https://lindeloev.github.io/tests-as-linear/ ). Some advocate to do that inference with bayes factors. Others, like discussed elsewhere in this thread, advocate combining the resulting posterior with a cost/value function, but either way the lesson is that there is less focus on "t-test-vs-anova" because they're the same thing anyways.
      - ivansavz 3y ago
        Thanks for the "Statistical Rethinking" recommendation. I had watched some of McElreath's lectures so I knew of the book, but next year I think I'm finally going to read it from end to end and follow along the 2024 course schedule: https://github.com/rmcelreath/stat_rethinking_2024#calendar--topical-outline https://github.com/rmcelreath/stat_rethinking_2024#calendar-... I had previously started the BDA course, which is another famous Bayesian course, see https://avehtari.github.io/BDA_course_Aalto/ https://avehtari.github.io/BDA_course_Aalto/ but I didn't finish it due to travel. No more excuses in 2024... time to level-up the Bayesian modelling skill ;)

The "more complicated" version of frequentist statistics is called robust statistics. There's most likely a way to rephrase your favorite Bayesian analysis so as to make it fully kosher from a "robust+frequentist" point of view, even keeping the math unchanged. It just goes to show how silly the "controversy" is.

PheonixPharts 3y ago

Bayesian statistics is fundamentally less complicated than Frequentist statistics since everything can be derived from a very simple set of first principles, rather than complex frameworks of ad hoc testing methodologies.

ivansavz 3y ago
> Bayesian statistics is fundamentally less complicated than Frequentist statistics [...] I broadly agree with you, but I'm wondering if you would reconsider your qualification as "less complicated" if you consider beginner learners. E.g. someone who knows basic descriptive statistics and probability theory, and is making first contact with inferential statistics. Specifically, assume a learner who knows what an integral is, but is far from proficient with it (UGRAD student, not a GRAD student). I was reading this paper[1] recently, which highlights two difficulties of teaching Bayesian stats: 1) the mathematical complexity of understanding conditional probability distributions, and 2) the lack of well defined, broadly accepted conventions for what priors to use in specific data analysis scenarios. I think a computational approach to prob theory could mitigate 1), but 2) remains a problem—the freedom to choose priors, is also a burden... [1] https://www.stat.purdue.edu/~dsmoore/articles/BayesPedagogy.pdf https://www.stat.purdue.edu/~dsmoore/articles/BayesPedagogy....
- ivansavz 3y ago
  For context, I'm not taking sides in the frequentist-vs-Bayesian debate, but coming from a practical problem: I'm working on a INTRO TO STATS book right now, and I would like to include a chapter on Bayesian statistics, but I'm not sure what specific analyses to showcase and recommend as "standard" approaches. Unlike the canonical t-tests and ANOVAs of frequentists, Bayesian statistics doesn't have canonical procedures (that I know of) that I can wholeheartedly recommend as "must know" and ready to use broadly. Maybe someone here might have suggestions? The closest thing that comes to mind is "Bayes factors," which has some traction (usage), but apparently they have lots of problems and limitations too, cf. https://www.youtube.com/watch?v=MqeWpR6S4XA https://www.youtube.com/watch?v=MqeWpR6S4XA
  - maltelau 3y ago
    Maybe you would find it useful to read a textbook on bayesian stats for inspiration. I can recommend Richard McElreath's "Statistical Rethinking" which makes it very clear how inflexible it is to just know recipes like t-tests or anovas. The canonical approach is to build a generative model with a parameter (or multiple for ~anova) that codes for the difference between groups and do inference on that parameter of interest. Most of the recipes taught in statistics classes can be modelled as a regression of some kind (this counts for frequentist stats too, see https://lindeloev.github.io/tests-as-linear/ https://lindeloev.github.io/tests-as-linear/ ). Some advocate to do that inference with bayes factors. Others, like discussed elsewhere in this thread, advocate combining the resulting posterior with a cost/value function, but either way the lesson is that there is less focus on "t-test-vs-anova" because they're the same thing anyways.
    - ivansavz 3y ago
      Thanks for the "Statistical Rethinking" recommendation. I had watched some of McElreath's lectures so I knew of the book, but next year I think I'm finally going to read it from end to end and follow along the 2024 course schedule: https://github.com/rmcelreath/stat_rethinking_2024#calendar--topical-outline https://github.com/rmcelreath/stat_rethinking_2024#calendar-... I had previously started the BDA course, which is another famous Bayesian course, see https://avehtari.github.io/BDA_course_Aalto/ https://avehtari.github.io/BDA_course_Aalto/ but I didn't finish it due to travel. No more excuses in 2024... time to level-up the Bayesian modelling skill ;)