Tim Sullivan, Zuse Institut Berlin

**"What is .. a well-posed Bayesian inverse problem?"**

Inverse problems, meaning the recovery of states or parameters in a mathematical model that match some observed data, are ubiquitous in applied sciences. They are also prime examples of ill-posed problems in the sense of Hadamard: either there is no solution in the strict sense, or there are multiple solutions, or the solution(s) depend sensitively upon the observed data and other parts of the problem specification. Regularisation of the inverse problem, whether deterministic or Bayesian, is intended to overcome these difficulties. This "What is...?" talk will outline the mathematical theory of well-posed Bayesian inverse problems for continuum quantities, exemplified by PDE-constrained inverse problems, as advanced by Andrew Stuart and collaborators over the last decade.