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We consider the history matching problem in a Bayesian setting. The link between the reservoir variables and the production history is given by a reservoir simulator. To run the reservoir simulator is a computer intensive task, and this severely limits the number of runs that can be made. It is therefore natural to consider the reservoir simulator as an unknown function with a corresponding prior distribution. We define an informative prior distribution for the reservoir simulator by combining a coarser (and thereby faster)version of the reservoir simulator with parameters correcting for the bias introduced by the coarser lattice. We simulate from the resulting posterior distribution by a Metropolis--Hastings algorithm. We case study inspired by the Troll field in the North Sea.<br>