We consider generalizations of the classical inverse problem to Bayesien type estimators, where the result is not one optimal parameter but an optimal probability distribution in parameter space. The practical computational tool to compute these distributions is the Metropolis Monte Carlo algorithm. We derive kinetic theories for the Metropolis Monte Carlo method in different scaling regimes. The derived equations yield a different point of view on the classical algorithm. It further inspired modifications to exploit the difference scalings shown on an simulation example of the Lorenz system.

翻译：我们将经典逆问题推广至贝叶斯型估计量，其中结果并非单一最优参数，而是参数空间中的一个最优概率分布。计算这些分布的实际计算工具是Metropolis蒙特卡洛算法。我们在不同标度区域推导了Metropolis蒙特卡洛方法的动力学理论。所推导的方程为经典算法提供了全新视角，并进一步启发了利用不同标度特性的改进方案，这通过洛伦兹系统的仿真示例得到了展示。