I like the thesis, but remember that decision theory is not the only difference between the frequentist and Bayesian frameworks. Crushing uncertainty is a useful prescription from frequentist epistemology, but Bayesianism and frequentism also disagree often on how uncertainty can be crushed. The Bayesian framework can account for a much wider variety of evidence (all of it, in the ideal), whereas frequentism can usually only utilize repetitive “iid” or controlled experimental data.
The real advantage of Bayesian analysis is drawing strong, high-certainty conclusions from bits of noisy data that a frequentist would just throw away. For instance, when decent priors are available, Bayesian analysis can draw very strong conclusions from very small data sets which a frequentist would dismiss as insignificant. I recently ran across a great example of this, which I will probably write up soon in a LW post.
Maybe I focused too much on the bayesianism vs frequentism thing. That’s not the point. You should use bayesian methods, just gather lots more data than locally necessary.
So yeah, sometimes that data is different types of evidence that a frequentist analysis couldn’t even correlate, but again, the point is to overdo it, not to disregard those many arguments or whatever.
I like the thesis, but remember that decision theory is not the only difference between the frequentist and Bayesian frameworks. Crushing uncertainty is a useful prescription from frequentist epistemology, but Bayesianism and frequentism also disagree often on how uncertainty can be crushed. The Bayesian framework can account for a much wider variety of evidence (all of it, in the ideal), whereas frequentism can usually only utilize repetitive “iid” or controlled experimental data.
The real advantage of Bayesian analysis is drawing strong, high-certainty conclusions from bits of noisy data that a frequentist would just throw away. For instance, when decent priors are available, Bayesian analysis can draw very strong conclusions from very small data sets which a frequentist would dismiss as insignificant. I recently ran across a great example of this, which I will probably write up soon in a LW post.
Maybe I focused too much on the bayesianism vs frequentism thing. That’s not the point. You should use bayesian methods, just gather lots more data than locally necessary.
So yeah, sometimes that data is different types of evidence that a frequentist analysis couldn’t even correlate, but again, the point is to overdo it, not to disregard those many arguments or whatever.