Abstract: A simple but naive way to fit a model to a given data or to solve an inverse problem is to match directly the sequence of observed data with the output of the model by minimizing some measure of mismatch between them. This approach can give satisfaction when the number of unknown parameters describing the solution is very small with respect to the number of independent data. In other cases, a prior knowledge on the solution is needed to find a satisfactory solution. The regularization theory then gives satisfactory solutions, but to deal with inaccuracies on data and uncertainties on models and to give some measure of the confidence on the solution is easier in a probabilistic approach. However, these two approaches are intimely related. The main object of this work is to present, in a simple and unifying way, this relation and discuss on the main limitations and advantages of each approach. !39
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