Numerical analysis of some Bayesian inverse problems - Quek, Jia Hao (2019)
Bayesian inverse problems for partial differential equations arise from many important real world applications. We find the physical properties of a medium in the form of an unknown coefficient of a partial differential equation, given limited noisy observations on the solution. The noise follows a known probability distribution. The unknown coefficient, or the parameters on which it depends, belong to a prior probability space. We aim to find the posterior probability which is the conditional probability of the unknown given the observations.