Alternatives to the MCMC method.
Sonderforschungsbereich 386, Discussion Paper 367
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.