**The
Hypotheses Reevaluation Math **

** **

From the logic and math point of view, there are two
alternatives and probabilities to consider **P(H), P(~H), P(H)+P(~H)=1**, namely: whether
macroscopic life on Mars is present (**H**), or it is not (**~H**).

According to the Bayes’ theorem, every
relevant observation **A** changes the *probabilities ratio***R=P(H)/P(~H)** of these two hypotheses:

** ** **R|A =
R*K(A), **where** K(A)=P(A|H)/P(A|~H)**

** **

For any two independent observations **A**, **B**,
holds **P(AB|**H**)=P(A|**H**)*P(B|**H**), **so we have

** **

** K(AB)=K(A)*K(B)**

** **

Consequently the *probabilities ratio* after taking
into account observations - is a product of initial *a priory*
probabilities ratio estimate, and of the correction coefficients for all
observations.

If we have enough observations, the initial bias of the hypothesis probability estimate does not really matter /if it is not zero/, since the corrections will eventually overcome it.

We will need more general rule based on the Bayes theorem:

** **

with **R(H)=P(H)/P(H0), R(H|A)=P(H|A)/P(H0|A), K(H|A)=P(A|H)/P(A|H0):**

** **

**R(H|A)=R(H)* K(H|A), K(H|AB)=K(H|A)*K(H|B) **

** **

**I(H|A)= -log(K(H|A)), I(H|AB)=I(H|A)+I(H|B) **

** **

** **