Which of the following statements is incorrect? “When making a decision under uncertainty, a Bayesian observer…”

Question

BlackTom AI · Accepted Answer

The question asks which statement is incorrect about how a Bayesian observer makes decisions under uncertainty, so we will evaluate each option in turn.
Option 1: '…weighs in both the prior and the likelihood information depending on their relative noise.' In Bayesian reasoning, both the prior and the likelihood contribute to the posterior, and their influence is modulated by how noisy or uncertain each source is. If the prior is noisier, its influence should be reduced, while a more reliable prior can have greater sway. Framing this in terms of relative noise aligns with the idea that credibility (noise/uncertainty) of each component determines its weight. This statement is reasonable.
Option 2: '…weighs in both the prior and the likelihood information depending on their relative precision.' Precision, the inverse of variance, is a core concept in Bayesian updating: higher precision (lower uncertainty) means greater weight in forming the posterior. This description matches standard Bayesian practice and is therefore correct.
Option 3: '…puts more weight on the likelihood information than the prior because the likelihood is based on the most recent information.' Although the likelihood can reflect new data, Bayesian updating does not automatically assign greater weight to the likelihood simply due to recency. The actual weighting depends on the relative precision (or reliability) of the prior and the data-generating process, not on recency alone. This statement is misleading because it attributes weight to recency rather than to quantified reliability/uncertainty metrics, making it the incorrect claim among the options.
Option 4: '…weighs in both the prior and the likelihood information depending on their relative reliability.' Reliability is closely tied to both uncertainty and accuracy; in Bayesian terms, both components influence the posterior in proportion to how trustworthy they are. This is a correct interpretation consistent with Bayesian updating.
In sum, the statements that align with Bayesian updating emphasize relative reliability, precision, or noise to determine the weighting of prior and likelihood, while the third option attributes weighting to recency alone, which is not a general Bayesian principle and therefore incorrect.

Which of the following statements is incorrect? “When making a decision under uncertainty, a Bayesian observer…”单项选择题

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