Barkley_Rosser
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"Yes," if Schrodinger's Cat is found to be dead; "no" if it is found to be alive.
Gotta have that continuous support too, which is the real key to converging on a cycle rather than a point.
In the fuzzier world of not a definite for-real underlying distribution, I note that multiple equilibria or basins in dynamical systems can give the multi-modality that within a herding framework can lead to some sort of cycle in bouncing back and forth between the dominant states.
Diaconis and Freedman.
Cyan,
Why should there be convergence to some such point when there is no underlying "true" distribution, either subjective or objective? Are you counting on herding by people? It is useful to keep in mind the conditions under which even in classical stats, Bayes' Theorem does not hold, for example when the underlying distribution is not continuous or if it is infinite dimensional. In the former case convergence can be to a cycle of bouncing back and forth between the various disconnected portions of the distribution. This can happen, presumably in a looser purely subjective world, with even a multi-modal distribution.
Cyan,
OK, I grant your point. However, assuming that there is some "subjectively real" probability distribution that the Bayes' Theorem process will converge is a mighty strong assumption.
The distinction here may be quite simple: an objective Bayesian accepts Bayes' Theorem, a subjective one does not. After all, Bayes' Theorem posits that repeated adjustments of priors based on new posterioris from the latest observations will asymptotically converge on the "true" probability distribution. That is only meaningful if one believes in an objective, "true" probability distribution (and of course assuming that certain necessary conditions hold regarding the underlying distribution and its dimensionality).
As someone whose parents knew Einstein as well as some other major "geniuses," such as Godel and von Neumann, I have long heard about the personal flaws of these people and their human foibles. Einstein was notoriously wrong about a number of things, most famously, quantum mechanics, although there is still research being done based on questions that he raised about it. It is also a fact that a number of other people had many of the insights into both special and general relativity, with him engaging in a virtual race with Hilbert for general relativity that he barely won. Quite a few had the basic ideas for special... (read more)
Eliezer,
Absolutely. Check out his ethnic dining guide of Washington (available on his website). His recommendations for Sichuan in Northern Virginia are indeed top notch, although I have heard it from some of his colleagues, who will remain nameless, that some of them are getting tired of getting dragged to some of these joints over and over with guest speakers... :-).
You might find my spoof of his guide amusing: "The Latest Washingtoon Ethnic Dining Guide," up on my website at http://cob.jmu.edu/rosserjb.
Eliezer,
Are you angling to become the new Tyler Cowen?
But I am deeply dishonored, having turned out to be the dead Schrodinger's Cat.