Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.

John W.Tukey, 1962

Central to this chapter is the concept of the state of information over a parameter set. It is postulated that the most general way to describe such a state of information is to define a probability density over the parameter space. It follows that the results of the measurements of the observable parameters (data), the a priori information on model parameters, and the information on the physical correlations between observable parameters and model parameters can all be described using probability densities. The general inverse problem can then be set as a problem of combining all of this information. Using the point of view developed here, the solution of inverse problems, and the analysis of uncertainty (sometimes called error and resolution analysis ), can be performed in a fully nonlinear way (but perhaps with a large amount of computing time). In all usual cases, the results obtained with this method reduce to those obtained from more conventional approaches.