tag:blogger.com,1999:blog-9959776.post115322736853866611..comments2021-06-16T20:59:35.476+01:00Comments on James' Empty Blog: More on detection, attribution and estimation 4: The LiteratureJames Annanhttp://www.blogger.com/profile/04318741813895533700noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-9959776.post-88547194486858495572007-03-02T09:56:00.000+00:002007-03-02T09:56:00.000+00:00Ooh, thanks for the great ref! I do think I've rea...Ooh, thanks for the great ref! I do think I've read it before but it's worth another look, and anyone else who finds this post is likely to find it interesting too.James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-55714260992190696812007-03-02T00:12:00.000+00:002007-03-02T00:12:00.000+00:00Thanks for the nice write-up.If you are not alread...Thanks for the nice write-up.<BR/><BR/>If you are not already familiar with it, you might be interested in reading <A HREF="http://bayes.wustl.edu/etj/articles/confidence.pdf" REL="nofollow">Jaynes's comprehensive article</A> on this topic - published in 1976!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9959776.post-1153634831860414162006-07-23T07:07:00.000+01:002006-07-23T07:07:00.000+01:00"the Bayesian fallacy"Doesn't ring a bell, but the..."the Bayesian fallacy"<BR/><BR/>Doesn't ring a bell, but there are various paradoxes and problems associated with Bayesian reasoning like the <A HREF="http://en.wikipedia.org/w/index.php?title=Doomsday_argument&oldid=64397706" REL="nofollow">Doomsday argument</A>. Since the bigest issue is generally in the unthinking adoption of a uniform prior as representing "ignorance" you'll not be surprised to find that I don't find them very convincing!James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-1153567862342328522006-07-22T12:31:00.000+01:002006-07-22T12:31:00.000+01:00What is "the Bayesian fallacy"? Was googling and ...What is "the Bayesian fallacy"? Was googling and came across this term. I have no stats training. Tone seemed to imply competing schools of thought and that Bayesians were like Albigensians fit only for the fire.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9959776.post-1153468478740001112006-07-21T08:54:00.000+01:002006-07-21T08:54:00.000+01:00Thanks for the link. I'm not sure that the conclus...Thanks for the link. I'm not sure that the conclusion is that startling though.<BR/><BR/>AIUI, the paper shows that frequentist (long-run) probability can never by itself dictate rational odds to a Bayesian making a finite number of bets, since (in the example presented) the Bayesian can always choose a prior that generates a particular initial set of outcomes that is not representative of the long term.<BR/><BR/>The example is instructive and reminds me of some issues in complexity theory and cryptography. The author uses the example of a pseudorandom number generator to generate coin tosses. Even though it has the correct long-run properties, an arbitrarily long initial series of H can be generated by initialising it appropriately. So if you are betting against an adversary who is using this machine, it may indeed be completely rational to refuse a series of bets on T even when offered "favourable" odds of better than 1:1. TBH, I don't find anything particularly unexpected or puzzling about this. Maybe no-one else had said it though!James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-9959776.post-1153320605198551162006-07-19T15:50:00.000+01:002006-07-19T15:50:00.000+01:00Browsing the web for the low-down on Charles Lyell...Browsing the web for the low-down on Charles Lyell, I came across this paper: <BR/>Max Albert, "Should Bayesians Bet Where Frequentists Fear to Tread?" Philosophy of Science, 72 (October 2005) pp. 584-593.<BR/>Abstract:<BR/>Probability theory is important not least because of its relevance for decision making, which also means: its relevance for the single case. The frequency theory of probability on its own is irrelevant in the single case. However, Howson and Urbach argue that Bayesianism can solve the frequentist's problem: frequentist-probability information is relevant to Bayesians (although to nobody else). The present paper shows that Howson and Urbach's solution cannot work, and indeed that no Bayesian solution can work. There is no way to make frequentist probability relevant.<BR/>http://www.journals.uchicago.edu/PHILSCI/journal/issues/v72n4/720401/brief/720401.abstract.html<BR/><BR/>You see I was actually being kind to you by not accepting your bet :-)Alastairhttps://www.blogger.com/profile/12102669780702913452noreply@blogger.com