Fundamental Tools for Statistical Inverse Problems

Abstract

This chapter deals with the fundamental statistical tools for solving statistical inverse problems that allow for identifying the stochastic models of uncertainties through the computational models. This part of the mathematical statistics is very well developed and there are a huge number of textbooks with which one can easily get lost when trying to learn. We have voluntarily limited the presentation to the basic ideas of the statistical inversion theory. Consequently, the nonstationary inverse problems such as the Bayesian filtering leading, for instance, to the linear Kalman filters and to the extended Kalman filters will not be presented.