I read this book in 2020, and the way this post serves as a refresher and different look at it is great.
I think there might be some mistakes in the log-odds section?
The orcs example starts:
We now want to consider the hypothesis that we were attacked by orcs, the prior odds are 10:1
Then there is a 1⁄3 wall-destruction rate, so orcs should be more likely in the posterior, but the post says:
There were 20 destroyed walls and 37 intact walls… corresponding to 1:20 odds that the orcs did it.
We started at 10:1 (likely that it’s orcs?), then saw evidence suggesting orcs, and ended up with a posterior quite against orcs. Which doesn’t seem right. I was thinking maybe “10:1” for the prior should be “1:10”, but even then, going from 1:10 in the prior to 1:20 in the posterior, when orcs are evidenced, doesn’t work either.
All that said, I just woke up, so it’s possible I’m all wrong!
Thanks, your confusion pointed out a critical typo. Indeed the relatively large number of walls broken should make it more likely that the orcs were the culprits. The 1:20 should have been 20:1 (going from −10 dB to +13 dB).
I read this book in 2020, and the way this post serves as a refresher and different look at it is great.
I think there might be some mistakes in the log-odds section?
The orcs example starts:
Then there is a 1⁄3 wall-destruction rate, so orcs should be more likely in the posterior, but the post says:
We started at 10:1 (likely that it’s orcs?), then saw evidence suggesting orcs, and ended up with a posterior quite against orcs. Which doesn’t seem right. I was thinking maybe “10:1” for the prior should be “1:10”, but even then, going from 1:10 in the prior to 1:20 in the posterior, when orcs are evidenced, doesn’t work either.
All that said, I just woke up, so it’s possible I’m all wrong!
Thanks, your confusion pointed out a critical typo. Indeed the relatively large number of walls broken should make it more likely that the orcs were the culprits. The 1:20 should have been 20:1 (going from −10 dB to +13 dB).