A note on the Karhunen-Lo\`eve expansions for infinite-dimensional   Bayesian inverse problems
  In this note, we consider the truncated Karhunen-Lo\`eve expansion for approximating solutions to infinite dimensional inverse problems. We show that, under certain conditions, the bound of the error between a solution and its finite-dimensional approximation can be estimated without the knowledge of the solution. 
Jinglai Li
math.ST math.NA stat.TH