Reevaluating Curtis Yarvin
A very reliable source has now told me that Curtis Yarvin’s SAT score at age 13 was 1540, and that his cited 167 IQ was not on the SMPY entrance exam, but on a separate test he took.
I was not told what score the IQ test was on or when he took it - assuming he was equally likely to take it between the ages of 5-45, the averaged regression coefficient should be 0.85 instead of 0.9 ((7*0.65+0.8*3+0.9*31)/41 - 0.65 is the regression coeff for children, 0.8 is the one for young teenagers, and 0.9 is the one for adults). I will also be treating any score within the simulation that lies between 149 and 189 as potentially being him, as these very high IQ scores tend to be not so reliable.
There is no apt reference population of 13 year old SAT takers, so I will continue to use the SMPY 1/10000 z-score that I conventionally use (3.719). That z-score will be treated as a cutoff, as he could be, realistically speaking, a 1/200000 or a 1/1000000 as well. I will be using a modified regression coefficient of 0.85*0.84 = 0.64 as he scored highly in both sections of the SAT.
The simulation ended with a mean of 154 and standard error of 8.
set.seed(25)
g <- rnorm(70000000, 0, 1)
c <- 0.714*g + rnorm(70000000)*sqrt(1-0.714^2)
d <- 0.85*g + rnorm(70000000)*sqrt(1-0.85^2)
subby1 <- data.frame(g, d)
subby1$c <- c
subby2 <- subset(subby1, (subby1$d > 47/15 & subby1$d < 87/15) & (subby1$c > 3.719))
mean(subby2$g)
sd(subby2$g)
qnorm(.65)
hist(subby2$g)
note - 0.85*0.84 → 0.85 is the stability, 0.84 in the corr between SAT and IQ
Your analysis is flawed. You computed the likelihood, not the most probable value. Given your assumptions, the most probable value is 150 +/- 4.2.
Second, when you dismiss values we have no evidence of (a '169' IQ score -- I mean, 69? 13^2? It's a joke) and add in evidence we know with certainty, you get a very different result.
When you consider that the g loading of years worth of writing must be pretty high (it's like a 4 year long test), and the fact that his writing is, say, 1.87 SD intelligence (midwit-tier cleverness), you get a predicted IQ of 136 +/- 1.19. So his IQ is in between 132 and 139 with high certainty.