Bayesian calibration of a numerical code for prediction

Field experiments are often difficult and expensive to make. To bypass these issues, industrial companies have developed computational codes. These codes intend to be representative of the physical system, but come with a certain amount of problems. Code validation is representative of one of these issues, related to the fact that the code intends to be as close as possible to the physical system. It turns out that, despite continuous code development, the difference between code output and experiments can remain significant. Two kinds of uncertainties are observed. The first comes from the difference between the physical phenomenon and the values recorded experimentally which is often represented by a white Gaussian noise. The second concerns the gap between the code and the physical system. To reduce this difference, often named model bias, or model error, computer codes are generally complexified in order to make them more realistic. These improvements lead to time consuming codes. Moreover, a code often depends on parameters to be set by the user to make the code as close as possible to field data. This estimation task is called calibration and can be performed with a time consuming or a fast code with or without model discrepancy. This paper provides a review of the main calibration methods developed to date. An application case will be used to illustrate the decisions taken along the article and to discuss divergence points. This example, motivated by an industrial and financial context, uses a code which predicts the power from a photovoltaic plant and will be used in a prevision context.