Estimating Probability of Life on Mars.

 

 

Methodology

 

We are going to apply the theory of based on observations hypotheses reevaluation, to the no-life on Mars hypothesis. We have to start from the higher margin of a priory probability of the no-life hypothesis, relative to the life hypothesis, for example R=100000.

 

Then the theory allows us to calculate the R after series of observations ABCDE…,

 

    R|ABCDE… = R * K(A) * K(B) * K(C) * K(D) * K(E) * …

 

                where K(X)=P(X|H)/P(X|~H)

 

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

 

Conditional probabilities of observed facts A, B, …  must be estimated from the available data. More precisely, we need centered or lower bound estimate under the life condition, and upper bound estimate under the no life condition.

 

 

Estimating hypothesis probability correction coefficients.

 

The objects of interest are those that appear, compared to others, the most likely to be of the biological origin. Such objects with practical certainty are of the biological origin, on the condition that life hypothesis is correct.

 

A target object is being presented as a base and a number of features. The base’s probability is being estimated from its relative observed frequency in the imagery.

 

The features’ probabilities are being estimated as conditioned on the base’s presence - using applicable physical considerations, and/or relative observed feature frequency in the imagery.

 

Under the no-life hypothesis features b, c, d … are independent:

       P(b, c, d ...)=p(b)*p(c)*p(d)…

 

Under the life hypothesis there is a relatively high conditional probability

       P(b, c, d...)=p(a)*P(c, d...|b)

 

We consider the K(~H|A) , with H being the life hypothesis and b the base feature:

 

K(~H|A)=( p(c)*p(d)*…) / P(c, d...|b)

 

To measure with sufficient precision the probabilities involved, we can count the pertinent objects, observed in the imagery.

 

 

Estimating particular observations.

 

 

Basic estimates:

Total relevant images 10,000

Image area size 10x10 m

Relevant objects in the area 10

 

Total covered area 1,000,000 m2

Total objects 100,000

Average object area 10 m2

 

Unique feature probability 1/10,000

 

 

Martian

 

K(~H|A) is estimated as probability of having a white, egg shape rock, of  size larger than base_size/10, on top of the black base rock.

 

Egg shape white rocks probability   < 1/100.

Egg shape white rocks count   < 1000.

Getting on top of base rock  < 1000 * 1/1,000,000 * 1/10=1/10,000

 

Suit feature probability  ~1/10,000  < 1/1000

K(~H|A)=1/10,000,000

 

 

Hooked creature

 

Hook feature probability  ~1/10,000 

K(~H|A)=1/10,000

 

                                                            The axe

 

K(~H|A)<1/10,000

 

The flowers

K(~H|A)<1/10,000

 

Berries on stalk

 

Bent stalk feature probability   <1/1000

Berry on a bent stalk << 1/1,000,000

Double 10^-18

 

K(~H|A)<10^-18

 

                                                            A girl

 K(~H|A)<1/10000

 

 

                                                            A girl head portrait

 K(~H|A)<10^-8

 

                                                            Coin

 K(~H|A)<1/10000

 

                                                The tree fossil

 

More than two unique features, prominently the blade

 K(~H|A)<< 10^-8

 

                                                            “Shell” on top

 K(~H|A)< 10^-4

 

                                                            “Cube”

 K(~H|A)< 10^-4

 

                                                            Horn

 K(~H|A)< 10^-4                          

 

 

 

 

                                                                   *      *      *

 

The current total no-life hypothesis probability reduction coefficient:

10^73

 

Using 3-sigma rule, estimate of lower limit of the no-life hypothesis probability reduction coefficient is:

10^24

 

 

 

*This section will expand, as the additional estimates are being done.