Bayesian analysis of hierarchical multifidelity codes. (English) Zbl 1280.62033
Summary: This paper deals with Gaussian process-based approximation of a code which can be run at different levels of accuracy. This method, which is a particular case of cokriging, allows us to improve a surrogate model of a complex computer code using fast approximations of it. In particular, we focus on the case of a large number of code levels on the one hand and on a Bayesian approach when we have two levels on the other hand. The main results of this paper are a new approach to estimating the model parameters which provides a closed form expression for an important parameter of the model (the scale factor), a reduction of the numerical complexity by simplifying the covariance matrix inversion, and a new Bayesian modeling that gives an explicit representation of the joint distribution of the parameters and that is not computationally expensive. A thermodynamic example is used to illustrate the comparison between 2-level and 3-level cokriging.
MSC:
62F15 | Bayesian inference |
68Q99 | Theory of computing |
65C60 | Computational problems in statistics (MSC2010) |
80A99 | Thermodynamics and heat transfer |