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Suppose you have pointed a telescope at a planet outside of our solar system, and observed some property of that planet (e.g. atmospheric composition). And suppose you want to know the probability of alien life on that planet given those observations, $P(\text{life} | \text{observation})$. Bayes' theorem says,

$$P(\text{life} | \text{observation}) = \frac{P(\text{observation} | \text{life}) P(\text{life})}{P(\text{observation})}$$

Applying the Law of total probability, we can say

$$P(\text{life} | \text{observation}) = \frac{P(\text{observation} | \text{life}) P(\text{life})}{P(\text{observation} | \text{life})P(\text{life}) + P(\text{observation} | \text{no life})P(\text{no life})}$$

I can imagine how someone might calculate the likelihoods, $P(\text{observation} | \text{life})$ and $P(\text{observation} | \text{no life})$. However, what about the prior, $P(\text{life})$?! People know very little about the probability of life on planets, or the probability of the origin of life.

My question: To determine the probability of life on another planet given some observation, is some estimation of the prior, $P(\text{life})$, required? or is it somehow avoidable?

Some relevant papers.

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    $\begingroup$ You cannot avoid having a prior if you're going to use a Bayesian approach. $\endgroup$
    – Galen
    Jul 12, 2021 at 1:47
  • $\begingroup$ Is there an alternative to a Bayesian approach? If yes, then how would this problem be asked in this alternative approach? $\endgroup$ Jul 12, 2021 at 3:01
  • $\begingroup$ Although the question doesn't require any approach or philosophy to be asked, in order to be answered it requires a sufficient combination of assumptions and data. Absent a Bayes prior (or other equivalent assumptions), you will need actual, representative data about extraterrestrial life -- which don't exist. (This was precisely the state of affairs until the last couple of decades: absent relevant observations, people simply made up assumptions and derived completely speculative, fanciful estimates of the probability of life elsewhere. Opinions inevitably ranged from zero up to 100%.) $\endgroup$
    – whuber
    Jul 12, 2021 at 13:20
  • $\begingroup$ Thanks. It sounds hopeless? How can astrobiologists and astronomers evaluate telescope observations for signs of life? Maybe an unbiased prior is possible? $\endgroup$ Jul 12, 2021 at 16:33

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