Use of the Bayesian statistics and the product of probabilities in the ionizing radiation field.

1) To show the validation criteria of the product of probabilities (PPs). Bayes' theorem (BT) is widely used in the ionizing radiation field; and 2) To demonstrate that terms P(B|A) and P (A|B) in the BT are not new probabilistic metrics, but the own respective probabilities of B and An events. Mathematical derivations based on strong probabilistic foundations, and with their respective illustrations. a) Determination of the validationcriteria of the PPs; and b) There is demonstration of incoherencies of the BT. 1) The tumor control probability (TCP) of independent radiation oncology treatments to patients with more than one target, calculated as the product of individual TCPs is an incoherent determination; 2) Given previously explained about BT terms, the use of this theorem should be re-considered; and 3). P (A∩B) P(A)*P(B) only when N × P(A) and N × P(B) are a subset of a population N, and if A and B are independent and simultaneous events. • It provides validation criteria of the product of probabilities (PPs). • The use of the Bayes' theorem should be re-considered. • UTCP = TCP × NTCP0 is an excellent example using PPs. • It provides a new proposal for the composite TCP expression. [ABSTRACT FROM AUTHOR]