Thanks. What do you think I should call it instead of Cox’s theorem? Should I just call it “Dutch book argument”?
For the complete class theorem, is the beef with my use of “strictly worse” when I really mean “weakly worse” / “at least as bad”? That was me being sloppy and I’ll fix it now, but let me know if there’s a further issue.
For the complete class theorem, is the beef with my use of “strictly worse” when I really mean “weakly worse” / “at least as bad”? That was me being sloppy and I’ll fix it now, but let me know if there’s a further issue.
Yup, “strictly worse” overstates things. Basically, the complete class theorem says the class of Bayesian minimum posterior expected loss estimators is the risk-Pareto frontier of the set of all estimators.
Thanks. What do you think I should call it instead of Cox’s theorem? Should I just call it “Dutch book argument”?
For the complete class theorem, is the beef with my use of “strictly worse” when I really mean “weakly worse” / “at least as bad”? That was me being sloppy and I’ll fix it now, but let me know if there’s a further issue.
Yeah, stick with “Dutch book”.
Yup, “strictly worse” overstates things. Basically, the complete class theorem says the class of Bayesian minimum posterior expected loss estimators is the risk-Pareto frontier of the set of all estimators.
Thanks!