1 Introduction Bayes theorem is the mathematical theorem used to revise probabilities in light of new evidence. For example, suppose that you think that some hypothesis has a 50% probability. Then you learn some fact that is twice as likely if the hypothesis is true as if it's false.
Then you learn some fact that is twice as likely if the hypothesis is true as if it's false. Now you should think that the theory has 2/3 probability. The simplest version of Bayes theorem uses odds ratios.
The simplest version of Bayes theorem uses odds ratios. Odds ratios tell you the ratio of the likelihood of one theory being true to the likelihood of it being false. For instance, a 2:1 odds ratio tells you that a theory is twice as likely to be true as false; a 3:2 odds ratio tells you that a theory has a 60% likelihood.