If you want, you might enjoy trying to guess what mistake I think I was making, before I spoil it for you.
Time to record my thoughts! I won’t try to solve it fully, just note my reactions.
For example, the first time I went to the Hot Tubs of Berkeley, a hot tub rental place near my house, I saw a friend of mine there. I wondered how regularly he went there. Consider the hypotheses of “he goes here three times a week” and “he goes here once a month”. The likelihood ratio is about 12x in favor of the former hypothesis. So if I previously was ten to one against the three-times-a-week hypothesis compared to the once-a-month hypothesis, I’d now be 12:10 = 6:5 in favor of it. This felt surprisingly high to me.
Well, firstly, I’m not sure that the likelihood ratio is 12x in favor of the former hypothesis. Perhaps likelihood of things clusters—like people either do things a lot, or they never do things. It’s not clear to me that I have an even distribution of things I do twice a month, three times a month, four times a month, and so on. I’d need to think about this more.
Also, while I agree it’s a significant update toward your friend being a regular there given that you saw them the one time you went, you know a lot of people, and if it’s a popular place then the chances of you seeing any given friend is kinda high, even if they’re all irregular visitors. Like, if each time you go you see a different friend, I think it’s more likely that it’s popular and lots of people go from time to time, rather than they’re all going loads of times each.
Another example: A while ago I walked through six cars of a train, which felt like an unusually long way to walk. But I realized that I’m 6x more likely to see someone who walks 6 cars than someone who walks 1.
I don’t quite get what’s going on here. As someone from Britain, I regularly walk through more than 6 cars of a train. The anthropics just checks out. (Note added 5 months later: I was making a british joke here.)
Time to record my thoughts! I won’t try to solve it fully, just note my reactions.
Well, firstly, I’m not sure that the likelihood ratio is 12x in favor of the former hypothesis. Perhaps likelihood of things clusters—like people either do things a lot, or they never do things. It’s not clear to me that I have an even distribution of things I do twice a month, three times a month, four times a month, and so on. I’d need to think about this more.
Also, while I agree it’s a significant update toward your friend being a regular there given that you saw them the one time you went, you know a lot of people, and if it’s a popular place then the chances of you seeing any given friend is kinda high, even if they’re all irregular visitors. Like, if each time you go you see a different friend, I think it’s more likely that it’s popular and lots of people go from time to time, rather than they’re all going loads of times each.
I don’t quite get what’s going on here. As someone from Britain, I regularly walk through more than 6 cars of a train. The anthropics just checks out. (Note added 5 months later: I was making a british joke here.)