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sigh Here we go again. Inferential statistics is unified by a field called decision theory, which is the mathematical formulation of how you choose a "good" map
by madhadron 14y ago
sigh Here we go again. Inferential statistics is unified by a field called decision theory, which is the mathematical formulation of how you choose a "good" mapping from the set of possible outcomes from your experiments to a set of possible decisions.
Bayesian and frequentist are interpretations of probability theory, nor are they the only ones (nor are all interpretations even concerned with a formalization of a notion of "chance"). They are not necessary to statistics.
- loup-vaillant 14y agoYou mean causal decision theory? Omega comes to you and presents two boxes. One is transparent and contains $1000. The other is opaque. Then Omega says "I give you 2 choices: either you take the two boxes, or you take only the opaque one. I have studied your brain, and have predicted your choice. If I have predicted that you will take only the opaque box, I have put $1M in it. If I have predicted you will take both boxes, I put nothing in it." Note that when Omega comes to you, the content of the opaque box is already fixed. So. What do you chose? Decision theory is not solved yet.