I A controversial application of Bayesian reasoning

AI Thread Summary
The discussion centers on the application of Bayesian reasoning to assess the likelihood of alien visitation based on independent reports of close encounters. It presents a mathematical model suggesting that with enough credible reports, the odds of aliens visiting Earth could significantly increase, specifically requiring 50 good cases to raise the odds by a factor of 10^15. However, the validity of this analysis hinges on the controversial assumption that alien and non-alien explanations are equally probable. This assumption is deemed speculative, leading to the closure of the thread due to a violation of forum rules against UFO speculation. The analysis, while mathematically sound, is ultimately considered flawed due to its reliance on unproven premises.
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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?
 
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p78653 said:
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.
 
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