We use a Markov chain prior Bayesian model to do lithology and fluid prediction from amplitude variations versus offset seismic data. We consider roughly the same model that is used in Larsen et al. (2006) which again is strongly influenced by the seismic inversion model found for example in Buland et al. (2005). We simulate from the resulting posterior distribution using a combination of the Metropolis--Hastings (MH) algorithm (Hastings, 1970) and the Gibbs sampler (Liu, 2001). We use the forward-backward algorithm (Liu, 2001) within the Metropolis--Hastings algorithm to update the elastic parameters and the lithology and fluid classes simultaneously. The result is an algorithm with very good convergence and mixing properties.<br>