One annoying thing in reading Chapter 3 -- chapter 3 states that for l=2,4,8, the optimal scoring rules can be written in terms of elementary functions. However, you only actually give the full formula for the case l=8 (for l=2 you give it on half the interval). What are the formulas for the other cases?
(But also, this is really cool, thanks for posting this!)
Thanks! I think the reason I didn’t give those expressions is that they’re not very enlightening. See here for l = 2 on (0, 1⁄2] and here for l = 4 on [1/2, 1).
Ha! OK, that is indeed nasty. Yeah I guess CASes can solve this kind of problem these days, can’t they? Well—I say “these days” as if it this hasn’t been the case for, like, my entire life, I’ve just never gotten used to making routine use of them...
One annoying thing in reading Chapter 3 -- chapter 3 states that for l=2,4,8, the optimal scoring rules can be written in terms of elementary functions. However, you only actually give the full formula for the case l=8 (for l=2 you give it on half the interval). What are the formulas for the other cases?
(But also, this is really cool, thanks for posting this!)
Thanks! I think the reason I didn’t give those expressions is that they’re not very enlightening. See here for l = 2 on (0, 1⁄2] and here for l = 4 on [1/2, 1).
Ha! OK, that is indeed nasty. Yeah I guess CASes can solve this kind of problem these days, can’t they? Well—I say “these days” as if it this hasn’t been the case for, like, my entire life, I’ve just never gotten used to making routine use of them...