Also, Yglesias lecturing people on uncertainty when it comes to interpreting polling data is laughable

Or, as written up in SIGBOIVK last year:

I have concluded that the gamma distribution has too many parameterizations and simply needs to chill, thank you

we have a slightly different formulation at work that gets around this --- I'll ping you on slack when I get online !

ooh! no, wasn't aware --- aside from the super simple sufficient forms (binomial & counts of poisson obs), I haven't done too much w/sufficiency (I've implemented a sufficient normal like one time remember it being a struggle lol)

oh yeah that's why my gut says that sum(x) ~ Gamma(n * alpha, theta) isn't a sufficient stat.

Link here shows what I get if I just repeatedly multiply the gamma pdf given new elements of x. Need to double check but it feels like this might actually give sufficiency?

bsky.app/profile/mark...

I haven't yet simulated, but IIRC my thinking was that by summarizing (x1, x2, ... xn) to sum(x), you lose some information in that there are many combinations of alpha/theta that can reasonably be fit to a single observation of sum(x)

oops xprod and xsum should index n here (xprod[n] & xsum[n])

moreso scary in the sense that I've got ptsd from thinking the sufficient normal was straightforward then banging my head against a wall until I got a working solution lol

(the sufficient normal was also my crash course in "sometimes the centered parameterization samples better")

point estimate probability says 100% chance of bayesian takeover 😈