From Observations to Hypotheses: Probabilistic Reasoning Versus   Falsificationism and its Statistical Variations
  Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of causes and effects. Formulated with Poincare's words, the "essential problem of the experimental method" becomes then solving a "problem in the probability of causes", i.e. ranking the several hypotheses, that might be responsible for the observations, in credibility. This probabilistic approach to the problem (nowadays known as the Bayesian approach) differs from the standard (i.e. frequentistic) statistical methods of hypothesis tests. The latter methods might be seen as practical attempts of implementing the ideal of falsificationism, that can itself be viewed as an extension of the proof by contradiction of the classical logic to the experimental method. Some criticisms concerning conceptual as well as practical aspects of na\"\i ve falsificationism and conventional, frequentistic hypothesis tests are presented, and the alternative, probabilistic approach is outlined. 
G. D'Agostini