Alternatives to the MCMC method

The Markov Chain Monte Carlo method (MCMC) is often used to
generate independent (pseudo) random numbers from a distribution
with a density that is known only up to a normalising constant.
With the MCMC method it is not necessary to compute the normalising
constant (see e.g. Tierney, 1994; Besag, 2000). In this paper we
show that the well-known acceptance-rejection algorithm also works
with unnormalised densities, and so this algorithm can be used to
confirm the results of the MCMC method in simple cases. We present
an example with real data.