Are there situations in which a frequentist approach is inherently better than Bayesian?

[R_cubed]

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Apart from a local culture in a domain, or there not being a Bayesian alternative, are there situations in which a frequentist approach shines, despite there being a reasonable Bayesian alternative?

Much of this dispute “between Bayes vs. Frequentists” is philosophical, and I’ve come to see as counter-productive. I would study a few of Sander Greenland’s posts in this forum (search for posts by @Sander or @Sander_Greenland ) who points out that the set of admissible Frequentist Procedures can also be considered Bayesian procedures.

Language for communicating frequentist results about treatment effects

The Bayes-frequentist debate enters the terminology debate especially when people start doing uncritical promotion of one or the other, because as I wrote before the dichotomy is disconnected from the details. The claims you put forth not only ignore abundant frequentist criticisms, but also disregard the vast diversity and divergences of methods and “philosophies” (or narrow dogmatisms) falling under the headings of “frequentist” and “Bayesian”. Fisherian frequentism in its most likelihoodist f…

Language for communicating frequentist results about treatment effects

Frank: This disagreement is central to the topic heading here as well as to its sister topic of communicating Bayesian results. In all this I am surprised by your failure to see the frequentist-Bayes mapping, which is key to proper use and description of both types of statistics. Please read Good (1987 at least; it’s one page). If we treat the hierarchical model used for your Bayesian odds (prior+conditional data model) as a two-stage (random-parameter) sampling model, we can compute a P-value …

This complete class theorem (which was only proved for parametric problems by Abraham Wald) was recently extended (using tools from mathematical logic, one of my other interests) to arbitrary (ie. infinite dimensional) problems.

https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-4/On-extended-admissible-procedures-and-their-nonstandard-Bayes-risk/10.1214/20-AOS2026.full

The TLDR summary is that historically (ie. the past 100 years), frequentist methods lead to computable techniques that could be implemented with very limited computing technology, and when properly used, can get you very close to a Bayesian result, without the risk of basing the analysis on erroneous prior information. This remains true in nonparametric situations, where the Bayesian solution is often extremely complex to compute (but that is changing).

Related Readings:
B. Efron (1986) Why Isn’t Everyone a Bayesian?, The American Statistician, 40:1, 1-5, DOI: 10.1080/00031305.1986.10475342 (link)

I continue to be influenced by Herman Chernoff’s comment on the paper:

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With the help of theory, I have developed insights and intuitions that prevent me from giving weight to data dredging and other forms of statistical heresy. This feeling of freedom and ease does not exist until I have a decision theoretic, Bayesian view of the problem … I am a Bayesian decision theorist in spite of my use of Fisherian tools.

Cobb, G. W. (2007). The Introductory Statistics Course: A Ptolemaic Curriculum? Technology Innovations in Statistics Education. Retrieved from

https://escholarship.org/uc/item/6hb3k0nz

See the discussion of this paper in this thread:

Random sampling versus random allocation/randomization- implications for p-value interpretation

I fail to see how that follows from what Sander wrote. The quote from Ernst in the Permutation Methods paper (who was also a co-author of the initial paper I linked to) described the problem: parametric assumptions that require large sample properties to hold for our finite, often very small sample, but we don’t know how quickly we converge to the limit. Philip Good in his book Permutation, Parametric, and Boostrap Tests of Hypotheses (3rd ed, p. 153-154) gave a real world example (categorica…

The first 20 min of this talk by Michael I Jordan on the relationship between Bayesian and Frequentist methods are instructive:

Bayesian or Frequentist, Which Are You? By Michael I. Jordan (Part 1 of 2)