We study how to optimize oil production with respect to revenue in a situation where the production rate is uncertain.
The oil production in a given period is described in terms of a difference equation, where this equation contains several uncertain parameters. The uncertainty about these parameters is expressed in terms of a suitable prior distribution. As the production develops, more information about the production parameters is gained, so the uncertainty distributions need to be updated.
However, the information we gather comes in the form of inequalities and equalities which makes it difficult to obtain exact analytical expressions for the posteriors. The solution is to use a combination of rejection sampling and the Metropolis-Hastings algorithm to estimate the distributions.