|WikiProject Statistics||(Rated Start-class, Low-importance)|
Why does this page exist?
This problem is equivalent to the problem of induction. I don't know why it has a separate page.
...What? Jaberwocky6669 16:21, Aug 9, 2004 (UTC)
- My thoughts exactly. From a Frequentist position (as I, apparently, hold), the question boils down to one of "how many days have there been where the sun hasn't risen?" Add to that the normal definition of a day: namely, an interval of time, at the beginning of which the sun rises; at some point during which, the sun sets; and at the end of which, the sun is just about to rise again. Then the question is a tautology -- it's not a day if the sun doesn't rise! Tomorrow is the day after today, and hey presto! the truth value of the statement "the sun will rise tomorrow" is certain, even if tomorrow doesn't happen.
- If you didn't follow the (fairly tight) argument, suffice it to say I don't think the question of the sun's rising tomorrow has any real meaning -- it *will* rise tomorrow, by definition and the laws of physics. Wooster 10:26, 27 Sep 2004 (UTC)
Not being a statistician, I found this article a bit difficult to follow. One difficulty concerns the difference between "probability" and "plausibility." The second sentence reads, "The sunrise problem illustrates the difficulty of using probability theory when evaluating the plausibility of statements or beliefs" (my emphasis). What, technically, is the distinction?
Also, I agree with Wooster, but would add this: This article displays the difficulty (or foolishness?) of trying to demonstrate a rigorous concept with an ill-defined example. I assume that the "problem" of whether the sun will rise tomorrow was chosen because the intuitive response is that the probability is 100%. The problem is interesting precisely because the offered statistical answer is so counter-intuitive. But looking more closely at the example (just what does it mean for the sun to "rise" "tomorrow"?) shows how muddy it is. If the point about statistics hasn't sunk in by that time (and it didn't for me), the use of an ill-defined example casts doubt on the worth of the whole exercise.
I also don't know whether this is a shortcoming of the "sunrise problem" itself, or only a shortcoming of how it is handled here.
--Old Nick 19:04, 5 Jan 2005 (UTC)
This is a very unhelpful and confused example of Bayesian reasoning. Bayesian reasoning requires specification of a prior probability and this may involve judgement and is thus controversial. There is a valid point to be made here about the difficulty of deriving prior probability from references examples. Trouble is, there is another component of Bayesian reasoning, namely the likelihood function. The likelihood is a mathematical model of how the data arise from some underlying chance process. The issue of an appropriate likelihood is being obscured here. Blaise 20:15, 22 December 2005 (UTC)
Nice article. It could be made clearer. For those who are puzzled: the fact that something has always been observed, doesn't guarantee that it will always happen in the future. The law of nature explain what we observed in the past, and keep explaining what we observe today. But there is no guarantee that they will not cease explaining observations tomorrow. Who can give us this guarantee? --pippo2001 21:54, 5 Jun 2005 (UTC)
I'm so out of it that even if the sun didn't come up tommorrow, then I wouldn't notice! Jaberwocky6669 00:21, Jun 26, 2005 (UTC)
I'm not so good at Bayesianism, but does this mean that the probability of survival increases as we get older? Every day I observe myself as alive should, by the logic in the article, increase the probability of my immortality. This is contrary to poular belief concerning mortality. Is this, however, correct reasoning according to Bayesianism? INic 00:47, 28 October 2005 (UTC)
Chapter 18 of Jaynes' book on Probability theory deals with this in detail; in viewing probability theory as generalised formal reasoning, we should not be surprised that a model gives nonsense if we don't feed it with all the correct data. The application of the rule of succession to sunrise ignores what we know about celestial mechanics; throwing away perfectly good information should always make us wary. Similarly, applying it to life expectancy, you would be ignoring what you know about biology and human life span. --genneth 00:21, 30 November 2005 (UTC)
"We just need a hypothetical random process that determines the fact that the sun will rise tomorrow or not. Based on past observations, we can infer the parameters of this random process, and from there evaluate the probability that the sun will rise tomorrow." I don't think randomness is necessary for the Bayesian concept of probability at all. Or rather, I'm quite sure it isn't. ;-) INic 22:41, 22 September 2006 (UTC)
- You are totally correct; this should be changed. Bayesian probabilities need not have anything to do with random processes, and indeed the description for the prior probability of the sun rising as having something to do with a hypothetical random process is totally wrong and misleading. For you and I the probability of the sun rising tomorrow is extremely close to one because we well understand the physics involved. A newborn child, however, who knows nothing of physics and has only been alive during the daytime, may well be justified in assigning a rather lower probability. (Bjfar (talk) 04:54, 22 November 2012 (UTC))
You're probalby forgetting the polar midnights. There likely are some people in the Amundsen-Scott base who would find this problem quite amusing. — Preceding unsigned comment added by 126.96.36.199 (talk) 19:16, 21 June 2011 (UTC)
One day, many suns
This section should pretty much just be removed I think. It makes no sense whatsoever to me. Why should the probability that a randomly selected star will explode before the morning have anything to do with the probability that our star will explode before then? At the very least we should restrict our selection to main-sequence stars of similar mass and age to our own, which of course result in a zero probability of impending nova, but I think this line of reasoning adds little to the article and obscures the philosophical foundation of the problem. (Bjfar (talk) 05:08, 22 November 2012 (UTC))
In the words of Bertrand Russell "It is obvious that if we are asked why we believe it the sun will rise to-morrow, we shall naturally answer, 'Because it always has risen every day'. We have a firm belief that it will rise in the future, because it has risen in the past. If we are challenged as to why we believe that it will continue to rise as heretofore, we may appeal to the laws of motion: the earth, we shall say, is a freely rotating body, and such bodies do not cease to rotate unless something interferes from outside, and there is nothing outside to interfere with thee earth between now and to-morrow. Of course it might be doubted whether we are quite certain that there is nothing outside to interfere, but this is not the interesting doubt. The interesting doubt is as to whether the laws of motion will remain in operation until to-morrow. If this doubt is raised, we find ourselves in the same position as when the doubt about the sunrise was first raised." (Problems of Philosophy, Chapter V "On Induction") (Bjfar (talk) 11:00, 22 November 2012 (UTC))