# DAE

## Seminar

### Bayesian Calibration of Computer Model Ensembles

Seminar Room 1, Newton Institute

#### Abstract

Using field observations to calibrate complex mathematical models of a physical process allows one to obtain statistical estimates of model parameters and construct predictions of the observed process that ideally incorporate all sources of uncertainty. Many of the methods in the literature use response surface approaches, and have demonstrated success in many applications. However there are notable limitations, such as when one has a small ensemble of model runs where the model outputs are high dimensional. In such instances, arriving at a response surface model that reasonably describes the process can be dicult, and computational issues may also render the approach impractical.

In this talk we present an approach that has numerous beneifts compared to some popular methods. First, we avoid the problems associated with defining a particular regression basis or covariance model by making a Gaussian assumption on the ensemble. By applying Bayes theorem, the posterior distribution of unknown calibration parameters and predictions of the field process can be constructed. Second, as the approach relies on the empirical moments of the distribution, computational and stationarity issues are much reduced compared to some popular alternatives. Finally, in the situation that additional observations are arriving over time, our method can be seen as a fully Bayesian generalization of the popular Ensemble Kalman Filter.

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