A controversial application of Bayesian reasoning

[p78653]

The gain in odds that aliens are visiting Earth (A) due to $n$ independent reports of close encounters (C) is given by:
$$\frac{\rm Odds(A|C)}{\rm Odds(A)}=\left[\frac{\rm Prob(C|A)}{\rm Prob(C|\bar A)}\right]^n.$$
Let us assume that we have good cases such that an alien explanation ($a$) is as likely as a non-alien explanation ($\bar a$):
$$\rm Prob(C\ \&\ a) = Prob(C\ \&\ \bar a).$$
Therefore
$$\rm \frac{Prob(C|A)}{Prob(C|\bar A)}=\frac{Prob(C\ \&\ \bar a)+Prob(C\ \&\ a)}{Prob(C\ \&\ \bar a)}=2.$$
Thus the gain in odds that aliens are visiting Earth is given by
$$\frac{\rm Odds(A|C)}{\rm Odds(A)}=2^n.$$
Accordingly we only need $50$ good cases of close encounters to raise the odds by a factor of $10^{15}$ which will overpower any reasonable prior bias against alien visitation.

Is this analysis correct?

 

[Nugatory]

Is this analysis correct?

No matter whether the application of Bayes' theorem is correct, the analysis is sensible only if we are allowed the assumption that "we have good cases such that an alien explanation ($a$) is as likely as a non-alien explanation ($\bar a$)" .

That assumption is inherently speculative so this thread violates the long-standing forum rule about UFO speculation and has been closed.