How do I best simulate an arbitrary univariate random variate using its probability function?

Question

In R, what\'s the best way to simulate an arbitrary univariate random variate if only its probability density function is available?

Answer 1

To clarify the "use Metropolis-Hastings" answer above:

suppose ddist() is your probability density function

something like:

n <- 10000
cand.sd <- 0.1
init <- 0
vals <- numeric(n)
vals[1] <- init 
oldprob <- 0
for (i in 2:n) {
    newval <- rnorm(1,mean=vals[i-1],sd=cand.sd)
    newprob <- ddist(newval)
    if (runif(1)

Notes:

1. completely untested
2. efficiency depends on candidate distribution (i.e. value of cand.sd). For maximum efficiency, tune cand.sd to an acceptance rate of 25-40%
3. results will be autocorrelated ... (although I guess you could always sample() the results to scramble them, or thin)
4. may need to discard a "burn-in", if your starting value is weird

The classical approach to this problem is rejection sampling (see e.g. Press et al Numerical Recipes)