Post date: Jul 08, 2020 8:19:15 PM
Pr(1,1|crooked casino) = probabilité d'obtenir un 1 suivi d'un autre 1 sur un dé en présupposant que le dé est truqué car le casino est malhonnête ("crooked").
Dans ce cas: on présuppose une cause (le casino est malhonnête) pour trouver la probabilité de l'action affectée.
So: this is moving from cause to effect - on présuppose la solution pour trouver la probabilité que ce soit vrai.
Bayes and Laplace realized it was possible to move back from effect to cause - on utilise les données pour savoir si c'est vrai.
Bayesian inference process:
1 - we have an idea about what the data looks like - prior
2 - we collect the data
3 - the model based on the prior is updated with the data
4 - we obtain the posterior
The idea is to give the probability of the hypothesis given the data obtained. The problem is that when we choose a probability model to describe the situation, we obtain the probability of obtaining the data given that the hyp is true". It is the opposite of what we want, we need to invert this probability. This problem is faced by both Frequentists and Bayesians. However, the Frequentists stop here: they use this inverse proba as evidence.
Frequentists: they assume the hyp is true, and based on this hyp they calculate a probability of having this data.