tag:blogger.com,1999:blog-3891434218564545511.post5569425311497714087..comments2024-03-27T20:37:09.185-05:00Comments on Alexander Pruss's Blog: Clumps and continuityAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-3891434218564545511.post-55977615308237655982014-10-16T12:10:26.269-05:002014-10-16T12:10:26.269-05:00I am no microbiologist but I can tell you that if ...I am no microbiologist but I can tell you that if someone feeds a subtype B event at location PH then there is almost a 100% chance of a subtype B event occurring at location PH the following day.Mark Rogershttps://www.blogger.com/profile/12691324025964108341noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-67893032700512406512014-10-16T09:45:55.132-05:002014-10-16T09:45:55.132-05:00Eric:
That line of thought would suggest that it&...Eric:<br /><br />That line of thought would suggest that it's an _a posteriori_ matter. But I am not confident of this.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-80104101718530818212014-10-16T09:34:46.880-05:002014-10-16T09:34:46.880-05:00I'll stick with the claim that, for things mov...I'll stick with the claim that, for things moving along continuous paths, proximity today is more closely related to proximity tomorrow. So that's still my response to your <i>original</i> point. Of course, you're right to point out that that's not sufficient for the more general question about the cat. But cat's surely don't move by Brownian motion. They aren't random (well, that's my bet). What the distribution is, that's an interesting question. But it's a question for animal behaviorists. (And I think there's been quite a bit of work on this - I recall such studies being applied to human movements too.) Eric Steinharthttps://www.blogger.com/profile/14998655729986164531noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-86720804654128019892014-10-16T06:20:29.751-05:002014-10-16T06:20:29.751-05:00Hey Dr. Pruss!
You say:
"And I wonder if it ...<br />Hey Dr. Pruss!<br />You say:<br /><br />"And I wonder if it has much to do with cats. Suppose we just have an event of some sort, but have no data on events of this sort except that we first got 398 events of subtype A and then 2 of subtype B. Should we have a high confidence, say 398/400=0.995, that the next event will be of subtype A? I think not. My intuition is that we should probably assign something around 0.5 to the next event being an A."<br /><br />So there should be low confidence that a subtype B event will occur since 2/400=0.005 yet since a subtype B event has occurred there is now a 0.5 level of confidence that it will occur again. So that while clumping may be rare, once it begins it's duration should not be surprising?Mark Rogershttps://www.blogger.com/profile/12691324025964108341noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-6886237286248304752014-10-15T23:48:53.296-05:002014-10-15T23:48:53.296-05:00The black cat who suddenly frequents your backyard...The black cat who suddenly frequents your backyard is clearly a familiar spirit who just appeared in the run-up to Halloween. Hopefully, this isn't a prelude to something more sinister, along the lines of Rosemary's Baby or The Omen. stevehttps://www.blogger.com/profile/16547070544928321788noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-8136318946266284642014-10-15T10:05:37.795-05:002014-10-15T10:05:37.795-05:00
Here is an interesting paper on how groups respon...<br />Here is an interesting paper on how groups respond to perceived clumping.<br /><br /><br />http://www.vanderbilt.edu/csdi/research/CSDI_WP_05-2013.pdfMark Rogershttps://www.blogger.com/profile/12691324025964108341noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-51983530033851698082014-10-15T09:24:08.670-05:002014-10-15T09:24:08.670-05:00Continuous paths by themselves don't lead to a...Continuous paths by themselves don't lead to a prediction of recurrence. continuous paths, I'd expect an ever-wider cut-off (cats move fast) Gaussian distribution of the cat's position centered on the last observed position (a Brownian motion with a speed limit). Such a distribution would predict that the cat would not be in the same place at the same time the next night.<br /><br />And I wonder if it has much to do with cats. Suppose we just have an event of some sort, but have no data on events of this sort except that we first got 398 events of subtype A and then 2 of subtype B. Should we have a high confidence, say 398/400=0.995, that the next event will be of subtype A? I think not. My intuition is that we should probably assign something around 0.5 to the next event being an A.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-34931911441968273132014-10-15T08:21:16.553-05:002014-10-15T08:21:16.553-05:00Cats move along continuous paths in space. Proxim...Cats move along continuous paths in space. Proximity today is more closely related to proximity tomorrow. I'm surprised you find this problematic.Eric Steinharthttps://www.blogger.com/profile/14998655729986164531noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-20477978483114366162014-10-15T06:19:47.617-05:002014-10-15T06:19:47.617-05:00Dr. Pruss,
Let's think about this. Halloween ...Dr. Pruss,<br /><br />Let's think about this. Halloween is upon us and very oddly a black cat has crossed your path three times. At the very least you should throw a pinch of salt over your left shoulder.Mark Rogershttps://www.blogger.com/profile/12691324025964108341noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-18970038511991037822014-10-14T22:48:08.373-05:002014-10-14T22:48:08.373-05:00Oh, and my prediction turned out correct. :-)Oh, and my prediction turned out correct. :-)Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-20487698362765418772014-10-14T22:47:54.493-05:002014-10-14T22:47:54.493-05:00That may be. I have a hard time thinking exactly *...That may be. I have a hard time thinking exactly *what* data that I have justifies it, though. Maybe general data that animal behavior tends to repeat?Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-19953369207543896242014-10-14T21:02:47.260-05:002014-10-14T21:02:47.260-05:00I would think the assumption that stray-cats-at-th...I would think the assumption that stray-cats-at-the-back-door events tend to clump is aposteriori justified. Other kinds of events tend not to clump (neighbor-mowing-his-grass events, say) and we learn that aposteriori too.Heath Whitehttps://www.blogger.com/profile/13535886546816778688noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-29298999743680458532014-10-14T20:04:47.276-05:002014-10-14T20:04:47.276-05:00Any prospector will tell you "Gold is where y...Any prospector will tell you "Gold is where you find it!"Mark Rogershttps://www.blogger.com/profile/12691324025964108341noreply@blogger.com