On 2025-04-24 1:33 p.m., Brian Smith wrote:
Hi Rui,
This code is able to generate absolutely correct random sample vector
based on the applicable constraints.
I have one question though.
If I understood the R code correctly then, the first element is
drawing random number from Uniform distribution unconditionally,
however drawing of sample point for the second element is conditional
to the first one. Therefore if we have large vector size instead of
current 2, I guess the feasible region for the last few elements will
be very small.
Will that be any problem? does there any algorithm exist where all
(n-1) elements would be drawn unconditionally assuming our vector has
n elements?
The answer could be yes or no depending on what you mean by "drawn
unconditionally".
If you mean "draw a coordinate that depends on previous coordinate
draws, and always accept it" then the answer is yes. You would modify
the limits of each draw depending on previous draws and the limits on
upcoming draws.
If you mean "draw each coordinate independently of previous draws", then
then answer is no, you can't do that except in a few very special cases.
Here's an example function:
rfixedsum <- function(n, sum, lower, upper) {
dim <- length(lower)
stopifnot(dim == length(upper), length(sum) == 1)
result <- matrix(NA, n, dim)
currentsums <- 0
for (i in 1:(dim-1)) {
# The highest following values could be is sum(upper[(i + 1):dim))
# The lowest they could be is sum(lower[(i + 1):dim)
lowlimit <- pmax(lower[i], sum - currentsums - sum(upper[(i + 1):dim]))
highlimit <- pmin(upper[i], sum - currentsums - sum(lower[(i +
1):dim]))
if (any(lowlimit > highlimit))
stop("sampling is impossible")
newvals <- runif(n, lowlimit, highlimit)
currentsums <- currentsums + newvals
result[,i] <- newvals
}
result[, dim] <- sum - currentsums
result
}
Duncan Murdoch
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