A tutorial on (Bayesian) probability

The aim of this tutorial is to show that, when properly formulated, probability theory is simply the science of plausible reasoning, which permits us to represent exactly and to update our state of information about the world. This is nothing new, since in 1812 Laplace wrote “[L]a théorie de la probabilité n’est au fond que le bon sens réduit au calcul: elle fait apprécier avec exactitude, ce que les esprits justes sentent par une sorte d’instinct, sans qu’il puissent souvent s’en rendre compte”. Unfortunately, the historical development of the field has deprived us of half of probability theory. It is now time to bring it back from neglect in order to realize Laplace’s claim and give us an indispensable tool for our technical endeavors and scientific investigations.