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It depends on if that's a realistic example or a toy example. Dreaded Anomaly Send a noteboard - 04/12/2011 05:32:34 PM
In the stereotypical example of reaching into a bag full of green and red marbles and withdrawing a marble, what's the proper representation of probability that the marble will be green or red? Do probabilistic functions like that just have limits approaching 100%?


In toy examples of probabilistic situations, we can consider all the information known, and then 100% seems like a legitimate probability. In reality, though, there is always some chance (maybe exponentially tiny, but still there) that we have some of the information wrong: maybe a cosmic ray hit one of our neurons, or one of our friends gave us a marble that spontaneously changes color just to mess with us. In this case, log-odds will helpfully differentiate between "very confident" and "infinitely confident." The amount of evidence we have is, by necessity, finite, so we must always leave room for our confidence to decrease when we get new information.

A few references for log-odds:
http://www.ncssm.edu/courses/math/Talks/PDFS/LOGODDS.pdf
http://dl.dropbox.com/u/34547557/log-probability.pdf

The first one uses an example of picking marbles to determine which of two barrels we have, if the distributions of marbles within the barrels is "known." The idea of "(deci)bels of evidence" becomes useful when considering this formulation.
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Scooby Doo and Secular Humanism. Stephen - 02/12/2011 09:58:49 PM 711 Views
Paraphrasing G.K. Chestertons famous affirmation of Christianity to justify secular humanism, eh? Joel - 02/12/2011 11:02:54 PM 433 Views
Love has nothing to do with spirituality or the supernatural; there is no universal meaning of life. Dreaded Anomaly - 03/12/2011 04:33:13 AM 503 Views
Those are legitimate beliefs, but not proven facts. Joel - 03/12/2011 10:05:44 PM 511 Views
Quite a combination of impossible standards, artificial categories, and misunderstandings of science Dreaded Anomaly - 04/12/2011 02:53:44 AM 515 Views
I have a question about log-odds formulation. Ghavrel - 04/12/2011 06:36:02 AM 303 Views
It depends on if that's a realistic example or a toy example. Dreaded Anomaly - 04/12/2011 05:32:34 PM 347 Views
That's pretty much what I thought. I meant in a toy example. Ghavrel - 04/12/2011 10:17:47 PM 297 Views
That's how I would use it, anyway. Dreaded Anomaly - 04/12/2011 10:41:01 PM 302 Views
Indeed Joel - 05/12/2011 11:05:41 PM 455 Views
Re: Indeed Dreaded Anomaly - 08/12/2011 02:25:13 AM 471 Views
Scooby Doo is not about secular fucking humanism. It's a Gnostic allegory. Tom - 02/12/2011 11:57:37 PM 394 Views
I had all but forgotten that post, one of the first I read at wotmania. Joel - 03/12/2011 10:09:36 PM 326 Views
Comparing me to Santa selling crack has positively made my day. Thank you! Tom - 05/12/2011 01:50:54 AM 443 Views
Not you, Scooby. Joel - 05/12/2011 11:09:45 PM 321 Views
Great article. *NM* Dreaded Anomaly - 03/12/2011 04:57:50 AM 226 Views
Scooby Doo, Secular Humanism or Gnostic allegory? Danu - 04/12/2011 12:36:09 AM 688 Views
You are welcome *NM* Stephen - 04/12/2011 01:50:41 AM 128 Views
but if you think about it Yunalesca - 04/12/2011 01:03:58 PM 310 Views
Have you seen the Tim Minchin video/song? Camilla - 04/12/2011 06:36:48 PM 421 Views
Look at the thread above this one. *NM* Dreaded Anomaly - 04/12/2011 06:59:40 PM 143 Views
What Dreaded Anomaly said *NM* Stephen - 04/12/2011 08:01:52 PM 152 Views
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