## The n ext crackpot iteration [Two-Stage / GS Designs]

Capt’n,

some remarks. More maybe tomorrow.

» The polynomial provides a fantastic approximation within our entire interval of interest.

Played around a little. Based on the AIC the 4th degree is the winner indeed.

» ##note: We might not want to write blah^3 etc if we optimize for speed, not sure.

Old wisdom. Here with my coefficients (total sample sizes [not N/seq], exact method for GRM 0.95, 80% power, CV 0.1–1.0).

library(microbenchmark) a <- c(5.897943, -40.988390, 603.109578, -338.281351, 70.43138) old.school <- function(a, CV) {   x <- a + a*CV + a*CV*CV + a*CV*CV*CV + a*CV*CV*CV*CV   x + (2 - x %% 2) } lazy <- function(a, CV) {   x <- a + a*CV + a*CV^2 + a*CV^3 + a*CV^4   x + (2 - x %% 2) } res <- microbenchmark(old.school(a, CV), lazy(a, CV), times=500L,                       control=list("random", warmup=10)) boxplot(res, boxwex=0.25, las=1) options(microbenchmark.unit="us") print(res)

» ## perhaps ceil would be better?

I would round up to the next even (as above).

» You see, the sample size estimates are sort of almost perfect already. If you want to remove the very few 1's and -1's then just increase the polynomial degree above.

That doesn’t help. With CV <- seq(0.1, 1, 0.01) I got a match in 46/91 and +2 in 45/91. OK, conservative.

Dif-tor heh smusma 🖖
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