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Everything that you've written is technically correct. But it seems like in the large majority of situations where people are using/publishing statistics, the e

by bjterry 12y ago

Everything that you've written is technically correct. But it seems like in the large majority of situations where people are using/publishing statistics, the expected value is what we care about but we are using frequentist methods. So if we are going to correct the "norm we use to choose our optimal procedure," it should imply a many-fold increase in uses of Bayesian methods. A huge amount of published papers that include any statistics are reporting means and p-values in very simple statistical analyses (essentially all papers published in the social sciences, health sciences, etc.). In many of these situations researchers could provide subjective priors based on the state of the research and knowledge beforehand and it would be philosophically valid and beneficial. Because of this mismatch, people who support Bayesian methods perhaps overstate their case. Maybe this is for the same reason that partisan political actors argue fervently for a single side of an issue, ignoring nuance. Nuance historically has not led to social change, and fixing statistics in science requires changing people's minds and "raising awareness."

keithwinstein 12y ago
I hear you, and my understanding is that this largely depends on the discipline. In fields like medicine and psychology, the flourishing of classical methods in the 30s and 40s and 50s did lead to a sort of dogmatism about p-values and a disdain for the old "inverse probability" (what we now call Bayesian methods) of the 18th and 19th centuries. These fields seem to be still recovering from this. My impression is that that's where you often find self-styled Bayesian rebels with the faith of the converted. In areas like radar or image processing or communications or information theory or ad placement or AI in general, I think the field has long had a more nuanced understanding of the underlying decision-theoretic concerns. When you have to win World War II and there is a cost to falsely identifying a Nazi aircraft as Allied, and a cost to falsely identifying an Allied aircraft as Nazi, you develop a notion of an ROC curve pretty quickly. Ditto when you want to talk to a Voyager probe and you're not sure if it just sent a 0 or a 1. In my view, the Bayesian vs. frequentist "debate" has little to say to these fields. Although for a contrary view, see what Jaynes writes about Shannon in "Probability Theory: The Logic of Science" in the last chapter ("Introduction to communication theory").

by bjterry 12y ago

keithwinstein 12y ago

I hear you, and my understanding is that this largely depends on the discipline. In fields like medicine and psychology, the flourishing of classical methods in the 30s and 40s and 50s did lead to a sort of dogmatism about p-values and a disdain for the old "inverse probability" (what we now call Bayesian methods) of the 18th and 19th centuries. These fields seem to be still recovering from this. My impression is that that's where you often find self-styled Bayesian rebels with the faith of the converted. In areas like radar or image processing or communications or information theory or ad placement or AI in general, I think the field has long had a more nuanced understanding of the underlying decision-theoretic concerns. When you have to win World War II and there is a cost to falsely identifying a Nazi aircraft as Allied, and a cost to falsely identifying an Allied aircraft as Nazi, you develop a notion of an ROC curve pretty quickly. Ditto when you want to talk to a Voyager probe and you're not sure if it just sent a 0 or a 1. In my view, the Bayesian vs. frequentist "debate" has little to say to these fields. Although for a contrary view, see what Jaynes writes about Shannon in "Probability Theory: The Logic of Science" in the last chapter ("Introduction to communication theory").