We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (possibly discontinuous) flux function are inferred from noisy measurements. In particular, the Lipschitz continuity of the measurement to posterior map as well as the stability of the posterior to approximations, are established with respect to the Wasserstein distance. Numerical experiments are presented to illustrate the derived estimates.

翻译：我们研究了巴耶斯群岛关于卡路里双曲保护法的逆向问题,从噪音测量中推断出关于初始数据量和(可能不连续的)通量函数等投入的统计资料,特别是,在瓦塞斯坦距离方面,确定了利普施茨对后方地图测量的连续性以及后方对近似值的稳定性。