Abstract: |
Recent research has been tending towards building models of uncertainty of the Earth, not just building a single (or few) detailed Earth models. However, just as any model, models of uncertainty often need to be constrained/conditioned to data to have any prediction power or be useful in decision making. In this presentation, I propose the concept of ?internal consistency? as a scientific basis to study prior (unconditional) and posterior (conditional) models of uncertainty as well as the various sampling techniques involved. In statistical science, internal consistency is the extent to which tests or procedures assess the same characteristic, skill or quality. In the context of uncertainty, I will therefore define internal consistency as the degree to which sampling methods honor the relationship between the unconditional model of uncertainty (prior) and conditional model of uncertainty (posterior) as specified under a (subjectively) chosen ?theory? (for example: Bayes? rule). The ?tests? performed are then various different ways of sampling from the same (conditional or unconditional) distributions. If these distributions are related to each other via a theory, then such ?tests? should yield similar results. I propose various such tests using Bayes? rule as the ?theory?. A first test is simply to generate unconditional models, extract data from them using a forward model and generate conditional models from this randomized data. Internal consistency with Bayes? rule would mean that both sets of conditional and unconditional models span the exact same space of uncertainty, simply because the data spans the uncertainty in the prior. I show that this not true for a number of popular conditional stochastic modeling methods: sequential simulation with hard data, gradual deformation and ensemble Kalman filters for solving inverse problems. I also show that in some cases lack of internal consistency leads to a considerable artificial reduction of (conditional) uncertainty that may have important consequences if such models are used for prediction purposes. A case involving predicting flow behavior is presented. Finally, I offer some discussion on the importance of internal consistency in practical applications and introduce some novel approaches to conditioning presented in other papers in this conference that are internally consistent as well as avoid the computational problems associated with McMC samplers. |
