- #1
p78653
- 3
- 1
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?
$$\frac{\rm Odds(A|C)}{\rm Odds(A)}=\left[\frac{\rm Prob(C|A)}{\rm Prob(C|\bar A)}\right]^n.$$
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?