Btw, there is some amount of philosophical convergence between this and some recent work I did on critical agential physics; both are trying to understand physics as laws that partially (not fully) predict sense-data starting from the perspective of a particular agent.
It seems like “infra-Bayesianism” may be broadly compatible with frequentism; extending Popper’s falsifiability condition to falsify probabilistic (as opposed to deterministic) laws yields frequentist null hypothesis significance testing, e.g. Neyman Pearson; similarly, frequentism also attempts to get guarantees under adversarial assumptions, as previously explained by Jacob Steinhardt.
Btw, there is some amount of philosophical convergence between this and some recent work I did on critical agential physics;
Thanks, I’ll look at that!
It seems like “infra-Bayesianism” may be broadly compatible with frequentism;
Yes! In frequentism, we define probability distributions as limits of frequencies. One problem with this is, what to do if there’s no convergence? In the real world, there won’t be convergence unless you have an infinite sequence of truly identical experiments, which you never have. At best, you have a long sequence of similar experiments. Arguably, infrabayesianism solves it by replacing the limit with the convex hull of all limit points.
But, I view infrabayesianism more as a synthesis between bayesianism and frequentism. Like in frequentism, you can get asymptotic guarantees. But, like in bayesiansim, it makes sense to talk of priors (and even updates), and measure the performance of your policy regardless of the particular decomposition of the prior into hypotheses (as opposed to regret which does depend on the decomposition). In particular, you can define the optimal infrabayesian policy even for a prior which is not learnable and hence doesn’t admit frequentism-style guarantees.
Btw, there is some amount of philosophical convergence between this and some recent work I did on critical agential physics; both are trying to understand physics as laws that partially (not fully) predict sense-data starting from the perspective of a particular agent.
It seems like “infra-Bayesianism” may be broadly compatible with frequentism; extending Popper’s falsifiability condition to falsify probabilistic (as opposed to deterministic) laws yields frequentist null hypothesis significance testing, e.g. Neyman Pearson; similarly, frequentism also attempts to get guarantees under adversarial assumptions, as previously explained by Jacob Steinhardt.
Thanks, I’ll look at that!
Yes! In frequentism, we define probability distributions as limits of frequencies. One problem with this is, what to do if there’s no convergence? In the real world, there won’t be convergence unless you have an infinite sequence of truly identical experiments, which you never have. At best, you have a long sequence of similar experiments. Arguably, infrabayesianism solves it by replacing the limit with the convex hull of all limit points.
But, I view infrabayesianism more as a synthesis between bayesianism and frequentism. Like in frequentism, you can get asymptotic guarantees. But, like in bayesiansim, it makes sense to talk of priors (and even updates), and measure the performance of your policy regardless of the particular decomposition of the prior into hypotheses (as opposed to regret which does depend on the decomposition). In particular, you can define the optimal infrabayesian policy even for a prior which is not learnable and hence doesn’t admit frequentism-style guarantees.