What is Sarah's prior probability for the hypothesis that the object is from earth (not from aliens)?

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The question asks: What is Sarah's prior probability for the hypothesis that the object is from earth (not from aliens)?

First, note that there are no answer options provided for this numerical question. Without a set of candidate choices, we cannot compare or rule out alternative priors directly. Instead, we can reason about what a prior probability means in this context.

Conceptual groundwork: In a Bayesian framework, the prior probability P(Earth) represents our belief about the object originating from Earth before observing any new evidence. It is a scalar between 0 and 1 that encodes previous knowledge, assumptions, or external information.

Interpreting a numeric value like 0.15: If Sarah’s prior is 0.15, that would imply a fairly skeptical stance at the outset, assigning only a 15% chance that the object is Earth-origin before looking at data about the object. This could reflect strong reasons to doubt Earth origin, such as prior observations suggesting alien signatures or a very low base rate of Earth-origin objects in a broader population.

How such a prior might be justified:
- Base rate considerations: If the probability of Earth-origin objects in the relevant population is known to be small, the prior could be correspondingly low. 
- Expert judgment: Reviewers may encode domain-specific beliefs (e.g., astronomical surveys, provenance evidence) that lead to a conservative prior.
- Conservatism or skepticism: In the absence of strong Earth-origin indicators, one might start with a modest prior like 0.15 to reflect caution.

What to consider if you had to decide the prior:
- What is the base rate of Earth-origin objects in this context? Is there reliable data to inform it?
- How strong is the prior evidence against Earth origin before observing the current object’s characteristics?
- How sensitive are the posterior conclusions to changes in the prior? If the analysis hinges heavily on the prior, you should examine a range of priors.

Important caveats: Since no answer options are listed, we cannot confirm whether 0.15 is the intended prior or whether alternative priors (e.g., 0.5, 0.01, 0.9) might be more appropriate given differing assumptions. Understanding the rationale behind chosen priors is more important than the exact numeric value in isolation, because priors influence updated beliefs, especially when data are weak or ambiguous.

COGSCI 200 001 WN 2025 Homework #1: Bayesian Inference

What is Sarah's prior probability for the hypothesis that the object is from earth (not from aliens)?

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