A mathematical model is a representation of a physical system depending on unknown parameters. Calibration refers to attributing values to these parameters, using observations of the physical system, acknowledging that the mathematical model is an inexact representation of the physical system. General Bayesian inference generalizes traditional Bayesian inference by replacing the log-likelihood in Bayes' theorem by a (negative) loss function. Methodology is proposed for the general Bayesian calibration of mathematical models where the resulting posterior distributions estimate the values of the parameters that minimize the L2 norm of the difference between the mathematical model and true physical system.
翻译:校准是指利用物理系统的观察将这些参数的值归为这些参数,同时承认数学模型不确切地代表物理系统。Bayesian将军的推论概括了传统的Bayesian推论,用一个(负的)损失函数取代Bayes' 理论中的日志相似值。建议了数学模型的Bayesian一般校准方法,由此得出的后表分布估计了参数值,以尽量减少数学模型与真实物理系统之间的L2标准差异。