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In statistics, **Bayesian inference** is a method of inference
in which Bayes' rule is used to update the probability estimate for a
hypothesis as additional evidence is learned. Bayesian updating is an important
technique throughout statistics, and especially in mathematical statistics:
Exhibiting a Bayesian derivation for a statistical method automatically ensures
that the method works as well as any competing method, for some cases. Bayesian
updating is especially important in the dynamic analysis of a sequence of data.
Bayesian inference has found application in a range of fields including science,
engineering, medicine, and law. [wikipedia]

Bayesian inference derives the probability as a result of two antecedents, a prior probability and a "likelihood function" derived from a probability model for the data to be observed. Bayesian inference computes the posterior probability according this equation:

Where:

· | means Given

·
H any *hypothesis* whose probability may be
affected by data

· E data that were not used in computing the prior probability

·
P(H) the *prior probability*, is the probability of H *before*
E is observed

·
P(H|E) the *posterior probability*, is the probability of H
*given* E, i.e., *after* E is observed

·
P(E|H) the probability of observing E *given* H, is also
known as the *likelihood*. Default: 0.5

· P(E) the marginal likelihood or "model evidence".

So;

P(H) is our new probability

P(H|E) is our starting point or prior probability

P(E|H) is the probability of our evidence or event (0.5).

P(E) is our “likelihood function” which is: P(E|H_{1})
* P(H_{1}) + P(E|H_{2}) * P(H_{2})

To make this work we need a starting point; one that should give the “anti” hypothesis greater weight. Since the DNA probabilities are the only indicators available; we shall start there.

In our “Real World Probabilities of Extraterrestrials on
Earth” paper we show the probability of ET being on Earth; at 7.1427 X 10^{-10}
or 0.00000000071427.

Applying this to our equation:

*Prior
probability:* 7.1427 X 10^{-10}

*New probability:*
5.36261 X 10^{-18} from the DNA data

0.5 * 7.1427 X 10^{-10} /
(7.1427 X 10^{-10} * 0.5) + (*5.36261
*X
10^{-18 }* 0.5) = **0.9999999924292286**

Our DNA data has changed to probability of me being ET to **0.9999999924292286** or 1: 1.00000000757077
making it an almost “sure thing”,

and making **the probability
of being Terrestrial:**** 0.00000000757077** or
1 in 132,086,960.77149.

While this is perhaps not the kind of “proof” many seem to want; it does serve to illustrate the Mathematical probabilities at play here.