tag:blogger.com,1999:blog-17232051.post4887264469970153190..comments2024-04-24T09:24:55.983-04:00Comments on Noahpinion: Bayesian SupermanNoah Smithhttp://www.blogger.com/profile/09093917601641588575noreply@blogger.comBlogger44125tag:blogger.com,1999:blog-17232051.post-21395959781408523172014-07-30T07:18:21.537-04:002014-07-30T07:18:21.537-04:00If you perform the same analysis, but with H repre...If you perform the same analysis, but with H representing the proposition "I will live to 100", then the same conclusion is reached (every bit of evidence I see increases the belief that I will live to 100), but in that case it seems entirely reasonable.<br /><br />The difference between the two hypotheses is that our prior belief that we will live to 100 is probably going to be much higher than our prior belief that we are invincible supermen. This means that out posterior belief that we are invincible supermen will only increase very slowly as we fail to die, but our posterior belief that we will live to 100 will rise rather faster.<br /><br />It seems to me that the Baysian approach here is doing the right thing, *provided* our prior beliefs are reasonable. Am I missing something?Dikran Marsupialnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-15887552133229659642014-07-29T02:32:38.176-04:002014-07-29T02:32:38.176-04:00from the perspective of the superman: how is this ...from the perspective of the superman: how is this problem different from the black swan?MSLhttp://princeton.edu/~mlachansnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-76588751648663347822014-07-28T20:05:58.869-04:002014-07-28T20:05:58.869-04:00I would be much more inclined to accept Bayseian R...I would be much more inclined to accept Bayseian Rationality if I wasn't an Orthodox Solipsist. Calming Influencehttps://www.blogger.com/profile/16093621031924205954noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-62218768194079977352014-07-28T06:23:00.103-04:002014-07-28T06:23:00.103-04:00uh?uh?Massimo Fuggettahttp://www.massimofuggetta.comnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-49994308877276226522014-07-27T08:31:19.684-04:002014-07-27T08:31:19.684-04:00What is your conclusive evidence for 'all livi...What is your conclusive evidence for 'all living things die'?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-40562285146107062032014-07-27T08:28:36.135-04:002014-07-27T08:28:36.135-04:00I am a critic of the naïve use of Bayes' rule,...I am a critic of the naïve use of Bayes' rule, but here I think I could defend Bayes.<br /><br />Mathematically, there seems to be a technical issue with the set of hypotheses. It is well known that the choice of coordinate system for a physical space can affect Bayesian inference. In Noah's example if one takes two hypotheses 'I will never die' and 'I will die some time' then the second hypothesis is compound so using the generalized likelihood (as per Good) one finds that the posterior probability of never dying does not increase the longer you survive.<br /><br />The problem with considering hypotheses such as 'I will die at age 45' using Bayes' rule naively is that one has to use some probability distribution for the time of death, so one is not comparing 'I will never die' with 'I will die sometime', but 'I will never die' with 'I have a typical life expectancy'. These two do not fill the space, hence Noah's odd result. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-8223802433778497612014-07-26T14:45:41.616-04:002014-07-26T14:45:41.616-04:00Even worse, like many Baysian economists, he confu...Even worse, like many Baysian economists, he confused events with their probabilities. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-75081235141920582862014-07-26T14:43:30.202-04:002014-07-26T14:43:30.202-04:00Confidence is a parameter in the equation that det...Confidence is a parameter in the equation that determines the number of heads in a raw needed to declare your coin biased. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-41693338713801445182014-07-25T18:21:24.943-04:002014-07-25T18:21:24.943-04:00No:
http://www.mayoclinic.org/diseases-conditions...No:<br /><br />http://www.mayoclinic.org/diseases-conditions/hemorrhoids/basics/definition/con-20029852Anonymoushttps://www.blogger.com/profile/02977684524676621423noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-73993281081055334512014-07-25T18:15:51.314-04:002014-07-25T18:15:51.314-04:00Massimo uncovered the strawmanMassimo uncovered the strawmanAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-24586725630511309932014-07-25T17:27:33.104-04:002014-07-25T17:27:33.104-04:00Econometrix: excellent pointEconometrix: excellent pointAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-30082966914430398262014-07-25T17:26:08.236-04:002014-07-25T17:26:08.236-04:00"Consider Proposition H: "God is watchin..."Consider Proposition H: "God is watching out for me, and has a special purpose for me and me alone. Therefore, God will not let me die."<br /><br />I just talked to him and he denied that. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-25572109964006027292014-07-25T12:12:05.408-04:002014-07-25T12:12:05.408-04:00Minor correction -- it cures homorrhoids. Not qui...Minor correction -- it cures homorrhoids. Not quite sure what they are, and I don't don't want to speculate much (human sterrhoids?), but if we map "e" --> "o" in one word, consistency or accuracy requires the same in the other word, eh?marcel proustnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-81252686868881624812014-07-25T11:55:53.408-04:002014-07-25T11:55:53.408-04:00I think this is very similar to Illusion of Contro...I think this is very similar to Illusion of Control Bias, and that happens to financial market people all the time. I made money on a trade => I’m a trading genius. That is why so many people quit their jobs to become day traders during the dot com bubble. Everybody looks like a genius when the market is rising. The Econometrixhttp://www.theeconometrix.comnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-90193997430389261162014-07-25T10:21:06.722-04:002014-07-25T10:21:06.722-04:00Noah,
Testing H requires a tug of war between conf...Noah,<br />Testing H requires a tug of war between confirmative evidence, such as "I am not dead so far" and disconfirmative evidence, such as "all living things die". In this case the latter evidence is conclusive, thus proving H false. Just looking at confirmative evidence to test a hypothesis is an instance of the Confirmation Bias.Massimo Fuggettahttp://www.massimofuggetta.comnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-55378482018415951142014-07-25T06:18:43.844-04:002014-07-25T06:18:43.844-04:00There is a mistake in defining E to simply be &quo...There is a mistake in defining E to simply be "not being killed" as time passes. This is true for every normal creature. To be a superman the evidence would need to be more like "not being killed in circumstances when ordinary beings would have been killed." <br /><br />Very unlikely you would observe evidence of that over time. You built in the result you wanted by your choice of E.Jeffrey Johnsonhttps://www.blogger.com/profile/07097567850607367929noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-7832078093635705372014-07-24T19:03:44.312-04:002014-07-24T19:03:44.312-04:00I don't see anything wrong with the reasoning ...I don't see anything wrong with the reasoning described in this post.<br /><br />JW Masonhttps://www.blogger.com/profile/10664452827447313845noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-53311041445602335462014-07-24T13:20:14.593-04:002014-07-24T13:20:14.593-04:00Ah ha. My prior, that a windbag would hold forth i...Ah ha. My prior, that a windbag would hold forth in these comments, is justified.Fixed Carbonhttps://www.blogger.com/profile/06321707907871138659noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-71133045087537603192014-07-24T13:13:04.676-04:002014-07-24T13:13:04.676-04:00This comment has been removed by the author.Fixed Carbonhttps://www.blogger.com/profile/06321707907871138659noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-17777822867244919722014-07-24T12:14:02.623-04:002014-07-24T12:14:02.623-04:00Amplifying another comment, epistemologically the ...Amplifying another comment, epistemologically the Bayesian Statistical Method is only a process for quantifying one's ignorance about a specific process. <br /><br />The author states: "But this gets into a philosophical thing that I've never quite understood about statistical inference, Bayesian or otherwise, which is the question of how to choose the set of hypotheses, when the set of possible hypotheses seems infinite."<br /><br />The set of possible hypotheses in ANY system of inference (whether it be classical statistics, the reading of tea leaves, metaphysical dogmatic systems (such as formal religions), measurement based dogmatic belief systems (such as science), consulting of oracles or bayesian statistics) is infinite because the set of possible outcomes in the world is infinite.<br /><br />So in the realm of statistics: classical method involves performing an experiment, collecting data at the end, performing tests of which 99% of practitioners haven't a clue what the underlying assumptions are, publishing standardized results (but only if they support your claim) which everyone understands but epistemologically shed little light on the topic researched. Classical conveniently ignores outliers to make it easier on the researcher. The trap here is that if your t-test is high the researcher then makes the epistemological leap that they've learned something new because they rejected the null hypothesis.<br /><br />With Bayesian Statistics the researcher must have a model and then with some rigor state their underlying assumptions before starting to collect data. As the data comes in outliers will be the most significantly weighted and the model will need constant updating. At the end of the experiment the researcher will have a better idea of their uncertainty around a certain process - but they will ALWAYS have uncertainty (just like humans do about anything in reality).<br /><br />Classical stats are perfect for writing scholarly papers. Bayesian stats are good for taking risk.<br /><br />p.s. The superman model in the article is simply a bad prior based upon a fallacy and ignoring a lot of relevant information.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-80539143136783744482014-07-23T17:59:40.052-04:002014-07-23T17:59:40.052-04:00Well, clearly "I have lived so far, therefore...Well, clearly "I have lived so far, therefore I will live forever" has a logic flaw but I think you are incorrect to attribute it to the gamblers fallacy. Essentially, the purported Bayesian superman is using his experience to try to determine whether the coin really is fair or if it is weighted in his favor. You're correct that a coin toss leading to five heads in a row shouldn't lead one to bet the farm on the sixth coming up heads, but how about after 100 heads in a row? If the proposition we are testing is "This coin is rigged to strongly favor heads", then our confidence in the assertion should indeed increase as the number of heads in a row increases. Is that really so different from the proposition that "my life is rigged to strongly favor my survival.? Granted, you'd want to give it a lot more then 100 tests before jumping off a bridge ...Anonymoushttps://www.blogger.com/profile/04238192025210567854noreply@blogger.comtag:blogger.com,1999:blog-17232051.post-29776349625772250982014-07-23T16:41:01.117-04:002014-07-23T16:41:01.117-04:00Unfortunately, your logic is flawed. First of all,...Unfortunately, your logic is flawed. First of all, we are dealing here with subjective probabilities. In reality, P(H) =0, so the analysis fails. But even if we accept the use of subjective probabilities, all you have shown is that the subjective probability P(E|H) > P(H). You have not shown that P(E|H) increases with each successive non-death. In fact, you make the classic "gambler's fallacy" mistake. You assume that past events (i.e. not dying in a number of dangerous occasions) affect the probability of future events. This is like saying that because a fair coin toss came up as five heads in the past, the probability of heads is higher on the subsequent toss.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-42100559686056166802014-07-23T15:06:23.217-04:002014-07-23T15:06:23.217-04:00Teenagers don't imagine god shielding them fro...Teenagers don't imagine god shielding them from risks. They simply underestimate risks.Tomnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-4459836096915010692014-07-23T13:47:05.339-04:002014-07-23T13:47:05.339-04:00The problem here is that the true Bayesian would u...The problem here is that the true Bayesian would understand that he himself is not special, and so therefore his prior must be based not on solely his own experiences, but on the likelihood of death based on past experiences of everyone. So the Bayesian would look at statistics of wearing a seatbelt and say "I better wear my seatbelt".... they wouldn't simply say "I've never worn my seatbelt and I'm still alive, therefore I don't need to wear my seatbelt." <br /><br />Another consequence of recognizing that a Bayesian would never use solely their own experience to form their prior is that every bayesian is forced to accept that the probability of eventual death is 1. <br /><br />Any Bayesian who would ignore all other experiences except their own is no real bayesian at all. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17232051.post-90926424887642921712014-07-23T08:56:21.109-04:002014-07-23T08:56:21.109-04:00Let us not forget that the Bayesian would be vindi...Let us not forget that the Bayesian would be vindicated the moment the subject dies...McKibbinUSAhttps://www.blogger.com/profile/10545798495680527622noreply@blogger.com