Alternatives to the neoBayesian Theorem, avoiding several of its   inconsistencies: The rMPE-Method
  Some drawbacks of the formalism of Bayes Theorem can be avoided by the rMPE-Method, a modification of the cMPE-Method that permits (i): Adding probabilities in spite of non-linearity. (ii): Taking into account extensional evidence and weight-bearing evidence that are mutually dependent, but opposed in their effects. (iii): Arriving at higher probabilities than by Bayes Theorem and (iv): Confirming also hypotheses that imply certain evidence. 
Rainer Gottlob