🤖 AI Summary
In Bayesian inverse problems, approximation errors in the measurement process model induce systematic bias, distorting the posterior distribution. This paper proposes a unified framework integrating transport maps with Bayesian model error modeling to jointly and adaptively estimate both the corrected posterior and the model error. The key innovation lies in constructing a differentiable transport map from a reference distribution to the bias-corrected posterior, while coupling it with a stochastic process representation of the model error to enable dynamic bias correction. The method is theoretically rigorous and computationally efficient. It is validated on two canonical indirect measurement problems, demonstrating significantly improved correction accuracy and sampling efficiency over conventional approaches. By explicitly accounting for structural model inadequacy, the framework effectively mitigates posterior distortion arising from model misspecification.
📝 Abstract
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior distribution in Bayesian inversion. We propose a unified framework that combines transport maps from a reference distribution to the posterior distribution with the model error approach. This leads to an adaptive algorithm that jointly estimates the posterior distribution of the measurand and the model error. The efficiency and accuracy of the method are demonstrated on two model problems, showing that the approach effectively corrects biases while enabling fast sampling.