More often than not, we encounter problems with varying parameters as opposed to those that are static. In this paper, we treat the estimation of parameters which vary with space. We use Metropolis-Hastings algorithm as a selection criteria for the maximum filter likelihood. Comparisons are made with the use of joint estimation of both the spatially varying parameters and the state. We illustrate the procedures employed in this paper by means of two hyperbolic SPDEs: the advection and the wave equation. The Metropolis-Hastings procedure registers better estimates.

翻译：与静态参数相比,我们经常遇到不同参数的问题。在本文件中,我们处理与空间不同的参数的估计。我们使用大都会-哈斯廷斯算法作为最大过滤可能性的选择标准。比较时使用对不同空间参数和状态的联合估计。我们用两个双曲的SPDE(对流和波方程)来说明本文件采用的程序。大都会-哈斯廷斯程序对更好的估计进行了记录。