R Under development (unstable) (2024-09-15 r87152 ucrt) -- "Unsuffered Consequences"
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> # Compare naive and uniform random sampling from beta + eta < 1
> # Uniform sampling is implemented in blim(..., randinit = TRUE).
> #
> # Last mod: Sep/12/2013, FW
> 
> nsamples <- 12000
> 
> ## The following naive algorithm samples non-uniformly from beta + eta < 1
> 
> beta <- runif(nsamples)
>  eta <- runif(nsamples, max=1 - beta)
> 
> plot(eta ~ beta, pch=".", main="Naive sampling")
> 
> ## The following algorithm samples uniformly from beta + eta < 1
> 
> beta <- runif(nsamples)
>  eta <- runif(nsamples)
> beta <- ifelse(beta + eta < 1, beta, 1 - beta)
>  eta <- ifelse(beta + eta < 1,  eta, 1 -  eta)
> 
> plot(eta ~ beta, pch=".", main="Uniform sampling")
> 
> 
> proc.time()
   user  system elapsed 
   0.40    0.03    0.43