Based upon the Bayesian framework for analyzing the discovery sequence in a play, a Markov chain Monte Carlo sampler—the Metropolis–Hastings algorithm, is employed to sample model parameters and pool sizes from their joint posterior distribution. The proposed sampling scheme ensures that the parameter space of changing dimension can be traversed in spite of the unknown number of pools. The equal sample weights make it easy to obtain the confidence intervals and assess the statistical error in the estimates, so that the statistical behaviors of the discovery process modeling can be well understood. Two application examples of the Halten play in Norwegian Sea and the Bashaw reef play in the Western Canada Basin show that, the computational advantage of this method to the simple Monte Carlo integration is considerable. In order to increase the convergence speed of the sample chains to the posterior distributions, several parallel simulations with different starting values are recommended.
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Sinding-Larsen, R., Xu, J. Bayesian Analysis of the Discovery Process Model Using Markov Chain Monte Carlo. Nat Resour Res 14, 333–344 (2005). https://doi.org/10.1007/s11053-006-9001-x
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DOI: https://doi.org/10.1007/s11053-006-9001-x