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

This is a comment but I don't have enough reputation to drop a comment to Ben Bolker's answer.

I am new to Metropolis, but IMHO this code is wrong because:

a) the newval is drawn from a normal distribution whereas in other codes it is drawn from a uniform distribution; this value must be drawn from the range covered by the random number. For example, for a gaussian distribution this should be something like runif(1, -5, +5).

b) the prob value must be updated only if acceptance.

Hope this help and hope that someone with reputation could correct this answer (especially mine if I am wrong).

# the distribution 
ddist <- dnorm
# number of random number
n <- 100000
# the center of the range is taken as init
init <- 0
# the following should go into a function
vals <- numeric(n)
vals[1] <- init 
oldprob <- 0
for (i in 2:n) {
  newval <- runif(1, -5, +5)
  newprob <- ddist(newval)
  if (runif(1) < newprob/oldprob) {
    vals[i] <- newval
    oldprob <- newprob
  } else vals[i] <- vals[i-1]
}
# Final view
hist(vals, breaks = 100)
# and comparison
hist(rnorm(length(vals)), breaks = 100)