Something that helped me understand where frequentist logic sat was Computer Age Statistical Inference. A lot of the tools of frequentism were developed for a time that is quite different to our own.
Just personally, I don't think frequentism is incompatible...it seems to have just been built up to frame everything in terms of a problem that is tractable (i.e. t-tests), and that is effective but comes with pitfalls. In economics, as an example, it seems that this toolset has gone pretty far.
What I like about Bayesianism, to my ill-informed mind, is that Bayes Theorem feels parallel to other parts of statistics that are effective: Kalman filters, Metropolis-Hastings, MDPs, even ELO is Bayesian (Glicko makes this explicit). And, this is in no way empirical but, when the results are directly comparable then I have seen better results (even when the Bayesian model is at an information deficit). No idea if that generalises beyond my activities (largely, sports modelling), there are still many pitfalls, and implementation can be tricky (I still don't understand Bayesian Data Analysis)...but it is pretty useful.
I am philosophically Bayesian, but given that I work with large datasets, I am practically frequentist.
I actually think that many of the people who promote Bayes everywhere have never tried to run a simple Stan regression on 100k+ data-points (pro-tip: sample, then sample some more, give up as it's taking too long).
That being said, from a philosophical point of view, Bayes is definitely the way I think.
In my org we frequently run Bayesian regression fitting on datasets of millions of samples.
The key is: don’t use pymc or stan for large data, just actually write your own MCMC code and write log likelihoods for your own models. It’s very easy and very fast, even in Python.
We do still use pymc and stan for other, smaller modeling tasks.
Yeah, but it's not worth it for my purposes. Given the kinds of data and the wide variety of problems we deal with, it would be an investment of too much resources relative to the rewards.
Just personally, I don't think frequentism is incompatible...it seems to have just been built up to frame everything in terms of a problem that is tractable (i.e. t-tests), and that is effective but comes with pitfalls. In economics, as an example, it seems that this toolset has gone pretty far.
What I like about Bayesianism, to my ill-informed mind, is that Bayes Theorem feels parallel to other parts of statistics that are effective: Kalman filters, Metropolis-Hastings, MDPs, even ELO is Bayesian (Glicko makes this explicit). And, this is in no way empirical but, when the results are directly comparable then I have seen better results (even when the Bayesian model is at an information deficit). No idea if that generalises beyond my activities (largely, sports modelling), there are still many pitfalls, and implementation can be tricky (I still don't understand Bayesian Data Analysis)...but it is pretty useful.