Accept/Reject Method for General Probability Distributions

• Let for .

  Let be any number .

  Generate x uniformly in .

  Generate r uniformly in .

  If , ignore x and start again.

  If , accept x.

• One can combine this with technique described on previous foils.

• Suppose and we generate x in distributed according to using exact method described first.

• This assumes we choose so that it can be integrated to find .

• Now use to accept-reject method or interpolation method with the probability distribution

• We choose so that it is roughly so that is more slowly varying than .