Why don’t more people know about the gem that is Tweedie's formula?
Say 𝐱 is a noisy measurement of 𝐮
𝐱 = 𝐮 + 𝐞
w/ 𝐞 ∼ 𝒩(𝟎, σ² 𝐈)
min mean² estimate of 𝐮 is 𝔼 [𝐮 | 𝐱]. Obviously we need the density P(𝐮|𝐱) right?
No! Tweedie says P(𝐱) is all you need!
1/2
@betanalpha @GuidoBiele @jbakcoleman I view SBC’s role parallel to that of defensive prior. Lesser evil, opt out. May I go one step further to argue “SBC:Valid workflow ~ KKT:Local optimum”? Hardly an iff relation which doesn’t detract KKT’s status as a cheap optimum litmus (with care)!
@betanalpha @GuidoBiele @jbakcoleman I wish to question the need to test individual posterior when our inference would not be based on its individual version, but rather on its pooled one. SBC as a function of experimental settings would help gauge reliability closet to granularity of its actual use.
@betanalpha @GuidoBiele @jbakcoleman I view SBC’s role parallel to that of defensive prior. Lesser evil, opt out. May I go one step further to argue “SBC:Valid workflow ~ KKT:Local optimum”? Hardly an iff relation which doesn’t detract KKT’s status as a cheap optimum litmus (with care)!
@betanalpha @GuidoBiele @jbakcoleman I wish to question the need to test individual posterior when our inference would not be based on its individual version, but rather on its pooled one. SBC as a function of experimental settings would help gauge reliability closet to granularity of its actual use.
@sp_monte_carlo Thanks, I wonder what might be the insight behind “symmetric distribution taking three possible values −√a, 0, √a, s.t. probability of a non-zero value is 1/a”. Three from knowing determining geometry.. Might 1/a * (√a)^2 =1 mean anything?