How to Choose Priors for Bayesian Estimation of the Discovery Process Model

The Bayesian version of the discovery process model provides an effective way to estimate the parameters of the superpopulation, the efficiency of the exploration effort, the number of pools and the undiscovered potential in a play. The posterior estimates are greatly influenced by the prior distribution of these parameters. Some empirical and statistical relationships for these parameters can be obtained from Monte Carlo simulations of the discovery model. For example, there is a linear relationship between the expectation of a pool size in logarithms and the order of its discovery, the slope of which is related to the discoverability factor. Some simple estimates for these unknown play parameters can be derived based upon these empirical and statistical conclusions and may serve as priors for the Bayesian approach. The priors and posteriors from this empirical Bayesian approach are compared with the estimates from Lee and Wang's modified maximum likelihood approach using the same data.