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> You're "pulling priors out of thin air" whether you realize it or not No, you are not. That’s an argument I often seen put forward by people who want the Bay

> You're "pulling priors out of thin air" whether you realize it or not No, you are not. That’s an argument I often seen put forward by people who want the Bayesian approach to be the one true approach. There are no prior whatsoever involved in a frequentist analysis. People who say that generally refer to MLE being somewhat equivalent to MAP estimation with a uniform prior in the region. That’s true but that’s the usual mistake I’m complaining about of reducing estimators to MLE. The assertion in itself doesn’t make sense. > Of course, Bayesian statistics also often involves assigning "uninformative" priors out of pure convenience That’s very hand wavy. The issue is that priors have a significant impact on posteriors, one which is often deeply misunderstood by casual statisticians.

addcommitpush 1y ago
Let’s say you run the most basic regression Y = X beta + epsilon. The X is chosen out of the set all possible regressors Z (say you run income ~ age + sex, where you also could have used education, location, whatever). Is that not equivalent to a prior that the coefficient on variables in Z but not in X is zero?
NeutralCrane 1y ago
Frequentists big complaint about priors are that they are subjective and influence the conclusions of the study. But the Frequentist approach is equivalent to using a non-informative prior, which is itself a subjective prior that influences the conclusions of the study. It is making the assumption that we know literally nothing about the phenomenon under examination outside of the collected data, which is almost never true.
tgv 1y ago
> There are no prior whatsoever involved in a frequentist analysis. It may not be everywhere, but even in the simplest case of NHST, there certainly is. It assumes no difference between H0 and H1. And NHST is basically the topic of this entire thread: it's what we should have stopped teaching a long time ago.

addcommitpush 1y ago

Let’s say you run the most basic regression Y = X beta + epsilon. The X is chosen out of the set all possible regressors Z (say you run income ~ age + sex, where you also could have used education, location, whatever). Is that not equivalent to a prior that the coefficient on variables in Z but not in X is zero?

NeutralCrane 1y ago

Frequentists big complaint about priors are that they are subjective and influence the conclusions of the study. But the Frequentist approach is equivalent to using a non-informative prior, which is itself a subjective prior that influences the conclusions of the study. It is making the assumption that we know literally nothing about the phenomenon under examination outside of the collected data, which is almost never true.

tgv 1y ago

> There are no prior whatsoever involved in a frequentist analysis. It may not be everywhere, but even in the simplest case of NHST, there certainly is. It assumes no difference between H0 and H1. And NHST is basically the topic of this entire thread: it's what we should have stopped teaching a long time ago.