OK I calculated the likelihoods of getting the full yeti revenue data set for those distributions and got the following results:
For 78-{age+1}d6 (which is equivalent to 71+1d6-{age}d6):
likelihood ~ 10^-192
For 72 + 1d5 - {age}d6:
likelihood ~10^-189
So the 1d5 version is literally 1000 times better fit to the data, and I doubt that the prior for 1d6 over 1d5 is that strong. Besides, the base value of 72 is a round number in a way, might increase the 1d5 prior a bit. I’d definitely bet on the 1d5 version over the 1d6.
That’s pretty convincing. Let’s try all the maybe-reasonable-ish versions:
71+1d6-{age}d6 has log[10] likelihood of −192.02 72+1d6-{age}d6 has log[10] likelihood of −190.57 72+1d5-{age}d6 has log[10] likelihood of −188.91 71+1d6-{age}d5 has log[10] likelihood of −196.42 72+1d6-{age}d5 has log[10] likelihood of −206.39 72+1d5-{age}d5 has log[10] likelihood of −200.41
Definitively -{age}d6, sure. Now here’s a much tighter question: what about 72+1d6-{age}d6? It takes a x45 hit on the likelihood compared to 72+1d5-{age}d6, which is pretty big, but I think I’m willing to say the chances of using a lone 1d5 right there are a bigger penalty. So my revised guess is 72+1d6-{age}d6.
OK I calculated the likelihoods of getting the full yeti revenue data set for those distributions and got the following results:
For 78-{age+1}d6 (which is equivalent to 71+1d6-{age}d6):
likelihood ~ 10^-192
For 72 + 1d5 - {age}d6:
likelihood ~10^-189
So the 1d5 version is literally 1000 times better fit to the data, and I doubt that the prior for 1d6 over 1d5 is that strong. Besides, the base value of 72 is a round number in a way, might increase the 1d5 prior a bit. I’d definitely bet on the 1d5 version over the 1d6.
That’s pretty convincing. Let’s try all the maybe-reasonable-ish versions:
71+1d6-{age}d6 has log[10] likelihood of −192.02
72+1d6-{age}d6 has log[10] likelihood of −190.57
72+1d5-{age}d6 has log[10] likelihood of −188.91
71+1d6-{age}d5 has log[10] likelihood of −196.42
72+1d6-{age}d5 has log[10] likelihood of −206.39
72+1d5-{age}d5 has log[10] likelihood of −200.41
Definitively -{age}d6, sure. Now here’s a much tighter question: what about
72+1d6-{age}d6?
It takes a x45 hit on the likelihood compared to
72+1d5-{age}d6, which is pretty big, but I think I’m willing to say the chances of using a lone 1d5 right there are a bigger penalty. So my revised guess is 72+1d6-{age}d6.
Nice analysis! But I am not so confident on how strong the prior should be and am somewhat torn on the conclusion.