Bottom-up Aggregation of Field-Level Oil Production Profiles via a Successive Sampling Discovery Model and a Birth Process: An Application to the Gulf of Mexico and Norway

Abstract We formulate a stochastic bottom-up model for the rate of oil production in a region by combining a size-biased sampling model of the discovery process (Barouch-Kaufman model), a birth process model for the discovery times, and field-level production profiles. For the size-biased sampling model we make the usual assumptions plus the assumption of a truncated field-size distribution and a Poisson prior distribution for the total number of fields. We then propose two approaches by which the size-biased sampling model can be formally connected to a model for the discovery times within a stochastic birth process framework. Using a truncated lognormal field-size distribution, parameter estimation via the expectation-maximization algorithm is repeated for the U.S. Gulf of Mexico and Norway based on the discovery history up to several different years. Combining the estimation results with the other components of the bottom-up model, we conduct Monte Carlo simulations for each region to derive the posterior distribution (conditioning on the discovery history) for the time path of the rate of oil production. JEL classification: Q35, Q47, C83, C63