Good post; this has way more value per minute spent reading and understanding it than the first 6 chapters of Jaynes, IMO.
There were 20 destroyed walls and 37 intact walls, leading to 10 − 3×20 − 1×37 = 13db
This appears to have an error; 10 − 3×20 − 1×37 = 10 − 60 − 37 = −87, not 13. I think you meant for the 37 to be positive, in which case 10 − 60 + 37 = −13, and the sign is reversed because of how you phrased which hypothesis the evidence favors (although you could also just reverse all the signs if you want the arithmetic to come out perfectly).
Also, nitpick, but
and every 3 db of evidence increases the odds by a factor of 2
should have an “about” in it, since 10^(3/10) is ~1.99526231497, not 2. (3db ≈ 2× is a very useful approximation, and implied by 10^3 ≈ 2^10, but encountering it indirectly like this would be very confusing to anyone who isn’t already familiar with it.)
Thanks! These are great points. I applied the correction you noted about the signs and changed the wording about the direction of evidence. I agree that the clarification about the 3 dB rule is useful; linked to your comment.
Edit: The 10 was also missing a sign. It should be −10 + 60 − 37. I also flipped the 1:20 to 20:1 posterior odds that the orcs did it.
Good post; this has way more value per minute spent reading and understanding it than the first 6 chapters of Jaynes, IMO.
This appears to have an error; 10 − 3×20 − 1×37 = 10 − 60 − 37 = −87, not 13. I think you meant for the 37 to be positive, in which case 10 − 60 + 37 = −13, and the sign is reversed because of how you phrased which hypothesis the evidence favors (although you could also just reverse all the signs if you want the arithmetic to come out perfectly).
Also, nitpick, but
should have an “about” in it, since 10^(3/10) is ~1.99526231497, not 2. (3db ≈ 2× is a very useful approximation, and implied by 10^3 ≈ 2^10, but encountering it indirectly like this would be very confusing to anyone who isn’t already familiar with it.)
Thanks! These are great points. I applied the correction you noted about the signs and changed the wording about the direction of evidence. I agree that the clarification about the 3 dB rule is useful; linked to your comment.
Edit: The 10 was also missing a sign. It should be −10 + 60 − 37. I also flipped the 1:20 to 20:1 posterior odds that the orcs did it.