tag:blogger.com,1999:blog-10584495.post4834213637430576377..comments2020-07-09T22:12:24.247-07:00Comments on dangerous idea: Surprisingness and evidence for supernatural occurrencesVictor Repperthttp://www.blogger.com/profile/10962948073162156902noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-10584495.post-2158363001443403042012-10-06T18:32:52.903-07:002012-10-06T18:32:52.903-07:00cl,
Sorry I dumped that on you. I got on my hobb...cl,<br /><br />Sorry I dumped that on you. I got on my hobby horse and took off at a gallop. This can only be adequately explained and discussed if you've studied probability theory and some philosophy of probability.<br /><br />"Now, if we're talking dice, or picking a card out of a stack, the concept of "probability" makes a little more sense, but... I would love a clear explanation of how one can say 100 heads in a row is just as likely as 45/55."<br /><br />It isn't. Notice that there is only one sequence of outcomes corresponding to 100 heads while there are lots of sequences corresponding to 45 heads. Each of these <i>particular</i> sequences is equally likely <i>given</i> that the coin is fair.<br /><br />The point of the thought experiment in equation is, "once I've tossed heads 100 times in a row, how likely is it that the coin is fair?" If the coin is fair, we should have expected the frequency of heads to be close to 50%. But the coin being heavily biased towards heads explains the results so far much better, so we might think that prob(heads)>1/2 when we start toss 101.Anonymoushttps://www.blogger.com/profile/10460814796782914633noreply@blogger.comtag:blogger.com,1999:blog-10584495.post-37508078766336758132012-10-06T14:01:46.137-07:002012-10-06T14:01:46.137-07:00I fixed it manually. I fixed it manually. Victor Repperthttps://www.blogger.com/profile/10962948073162156902noreply@blogger.comtag:blogger.com,1999:blog-10584495.post-87459095212473216302012-10-06T14:01:42.945-07:002012-10-06T14:01:42.945-07:00cl,
Perhaps I can shed a little light on the prob...cl,<br /><br />Perhaps I can shed a little light on the probability question.<br /><br />If you toss a coin 100 times, there are many trillions of possible sequences. Only one of those sequences consists of all heads. There are many sequences that consist of a mixture of heads and tails, but if you specify the exact order of the sequence, there is only one way to get that, so its probability is the same as all heads. On the other hand if you don't care about the order, there are many ways to get some heads and some tails. So the probability of that is much greater than all heads.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10584495.post-44912214513431365822012-10-06T13:40:27.081-07:002012-10-06T13:40:27.081-07:00I hate to say this, because this isn't a criti...I hate to say this, because this isn't a critique of the substance of your post. However the formatting is attrociously ugly. There's a paragraph separation between each and every line. There's more white space than text.Leonhardhttps://www.blogger.com/profile/13815705241524089233noreply@blogger.comtag:blogger.com,1999:blog-10584495.post-30661375853212209622012-10-05T21:46:45.339-07:002012-10-05T21:46:45.339-07:00Cl,
"I really don't think "probabil...Cl,<br /><br />"I really don't think "probability" is real or even applies in this case. I can flip a small dish and make it land heads every time. There's no "probability" there, it's all in the throw. Why should this change because the dish gets smaller?"<br /><br />You can always use historic results (repeat trials and then count the number of hits over n) to create a probability distribution for real-world applications. In that case, the probability distribution for your small dish would be different than the one for the coin. The probability distribution for someone who is trained to throw dice a certain way for craps would be different from the average user. It's still the same problem, just harder for the player to insert bias into the equation. However, for theoretical purposes, the assumption of there not being bias (for the instrument itself and in the throw) is included, but there are ways to test this assumption in applications.Kevinhttps://www.blogger.com/profile/09006028835831638046noreply@blogger.comtag:blogger.com,1999:blog-10584495.post-16855734689202383412012-10-05T21:26:08.166-07:002012-10-05T21:26:08.166-07:00cl,
I'll take a stab at it.
You may be mixin...cl,<br /><br />I'll take a stab at it.<br /><br />You may be mixing up two different things: a particular series of results of 100 coin tosses, and a general grouping of proportional results.<br /><br />Think of it this way. Imagine instead of 100 heads in a row, you get 99 heads, 1 tails.<br /><br />But there's 100 different ways to get that. (heads, tails, tails, [...] tails) or (tails, heads, tails, tails, [...] tails) or (tails, tails, heads, tails, tails [...] tails), etc.<br /><br />There's a difference between talking about "I got series 1, which was tails, then 99 heads" which describes a specific series, and "I got 99 heads and 1 tails", which describes 100 different series.Crudehttps://www.blogger.com/profile/04178390947423928444noreply@blogger.comtag:blogger.com,1999:blog-10584495.post-89568469354627321422012-10-05T21:20:00.396-07:002012-10-05T21:20:00.396-07:00Zachary,
Thanks for the effort, sincerely, but......<b>Zachary</b>,<br /><br />Thanks for the effort, sincerely, but... that was and this is still pure gibberish for me. I honestly think those guys are just talking out their backside, and yes, I realize many people esteem them as great minds. I really don't think "probability" is real or even applies in this case. I can flip a small dish and make it land heads every time. There's no "probability" there, it's all in the throw. Why should this change because the dish gets smaller?<br /><br />Now, if we're talking dice, or picking a card out of a stack, the concept of "probability" makes a little more sense, but... I would love a clear explanation of how one can say 100 heads in a row is just as likely as 45/55.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10584495.post-9061269317164466102012-10-05T21:02:14.793-07:002012-10-05T21:02:14.793-07:00"Is that bolded part correct? I'm no prob..."Is that bolded part correct? I'm no probability expert, but that strikes me as wrong. Isn't the whole point that 100 heads in a row is actually less likely than most other combinations (say, 60/40 or 55/45)?"<br /><br />It's correct if you consider the order. As in, there are 100 different ways to flip 99 heads and 1 tail and those 100 ways have an equal chance of occurring. If you disregard order, then 100 and 0 heads are the least likely.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10584495.post-59512483713133343562012-10-05T20:43:30.900-07:002012-10-05T20:43:30.900-07:00cl,
On the assumption that the coin is fair and t...cl,<br /><br />On the assumption that the coin is fair and the further assumption that this assumption is not at all doubted, Reppert is correct.<br /><br />Now, suppose we've tossed a coin 99 times and landed heads each time. We might then suspect that the coin is biased towards heads, since if we are not certain that the coin is fair we update the expected frequency of heads in accordance with this evidence.<br /><br />There's a bloggingheads discussion between Andrew Gelman and Eliezer Yudkowsky which opens with this problem: http://bloggingheads.tv/videos/2296Anonymoushttps://www.blogger.com/profile/10460814796782914633noreply@blogger.comtag:blogger.com,1999:blog-10584495.post-87922770784989283992012-10-05T19:40:10.515-07:002012-10-05T19:40:10.515-07:00Hi Vic. I've a question:
If I were to flip a ...Hi Vic. I've a question:<br /><br /><i>If I were to flip a coin 100 times and get heads every time it would surprise me, <b>even though any other sequence of heads and tails would be equally unlikely</b>.</i><br /><br />Is that bolded part correct? I'm no probability expert, but that strikes me as wrong. Isn't the whole point that 100 heads in a row is actually <i>less likely</i> than most other combinations (say, 60/40 or 55/45)?Anonymousnoreply@blogger.com