Generate n samples, Rejection sampling in R

Question

Rejection Sampling

Im working with rejection sampling with a truncated normal distribution, see r code below. How can I make the sampling stop at a specific n? for example 1000 observations. I.e. I want to stop the sampling when the number of accepted samples has reached n (1000).

Any suggestions? Any help is greatly appreciated :)

#Truncated normal curve    
curve(dnorm(x, mean=2, sd=2)/(1-pnorm(1, mean=2, sd=2)),1,9)

#create a data.frame with 100000 random values between 1 and 9

sampled <- data.frame(proposal = runif(100000,1,9))
sampled$targetDensity <- dnorm(sampled$proposal, mean=2, sd=2)/(1-pnorm(1, mean=2, sd=2))

#accept proportional to the targetDensity

maxDens = max(sampled$targetDensity, na.rm = T)
sampled$accepted = ifelse(runif(100000,0,1) < sampled$targetDensity / maxDens, TRUE, FALSE)

hist(sampled$proposal[sampled$accepted], freq = F, col = "grey", breaks = 100, xlim = c(1,9), ylim = c(0,0.35),main="Random draws from skewed normal, truncated at 1")
curve(dnorm(x, mean=2, sd=2)/(1-pnorm(1, mean=2, sd=2)),1,9, add =TRUE, col = "red", xlim = c(1,9),  ylim = c(0,0.35))



X <- sampled$proposal[sampled$accepted]

How can I set the length of X to a specific number when I sample?

Answer 1

After sleeping on it, if you're determined to use rejection sampling and only doing it until 1,000 have passed, I don't think there's a better option than just using a while loop. This is significantly less efficient than

sampled$accepted = ifelse(runif(100000,0,1) < sampled$targetDensity / maxDens, TRUE, FALSE)
X <- sampled$proposal[sampled$accepted][1:1000]

The time taken for the above code is 0.0624001s. The time taken for the code below is 0.780005s. I include it because it is the answer to the specific question you've asked, but the approach is inefficient. If there's another option I'd use that.

#Number of samples
N_Target <- 1000
N_Accepted <- 0

#Loop until condition is met
i = 1
sampled$accepted = FALSE
while( N_Accepted < N_Target ){

    sampled$accepted[i] = ifelse(runif(1,0,1) < sampled$targetDensity[i] / maxDens, TRUE, FALSE)
    N_Accepted = ifelse( sampled$accepted[i], N_Accepted + 1 , N_Accepted )
    i = i + 1
    if( i > nrow( sampled ) ) break

}