Which of the following statements is TRUE about the weight placed on information in respect to its reliability?

Question

BlackTom AI · Accepted Answer

Bayesian updating combines prior knowledge and new sensory evidence by weighting each source according to its reliability (more reliable = greater weight).

Relevant concepts: Bayes’ rule states posterior ∝ prior × likelihood. In continuous Gaussian cases, reliability is captured by precision (inverse variance). For a prior N(μ0, σ0^2) and sensory likelihood N(μL, σL^2), the posterior is Gaussian with mean equal to a precision-weighted average of μ0 and μL.

Step-by-step derivation (Gaussian case):
1. Prior precision = 1/σ0^2, likelihood precision = 1/σL^2.
2. Posterior precision = 1/σpost^2 = 1/σ0^2 + 1/σL^2.
3. Posterior mean μpost = (μ0/σ0^2 + μL/σL^2) / (1/σ0^2 + 1/σL^2).
Rewriting: μpost = w0·μ0 + wL·μL where w0 = (1/σ0^2) / (1/σ0^2 + 1/σL^2) and wL = (1/σL^2) / (1/σ0^2 + 1/σL^2). These weights sum to 1 and are proportional to precision—thus the more precise (less noisy) source gets more weight.

Numerical example: μ0 = 0, σ0 = 2 (precision 0.25); μL = 5, σL = 1 (precision 1). Weights: wL = 1/(1+0.25) = 0.8, w0 = 0.25/1.25 = 0.2. Posterior mean = 0.8·5 + 0.2·0 = 4. The more reliable sensory cue dominates the estimate.

Why the correct option is correct: It directly states that Bayesian observers assign greater weight to the source with higher reliability, which is exactly what the precision-weighted posterior mean shows.

Why the other options are incorrect:
- "More weight on sensory because it’s less reliable" is contradictory: less reliable means lower weight, not higher.
- "More weight on prior because it’s less reliable" likewise reverses the reliability-weight relationship.
- "Make a random guess because info is never 100% reliable" mischaracterizes Bayesian inference; uncertainty is handled probabilistically, not by random guessing.

Conclusion: The correct choice is "Bayesian observers put more weight on the source of information that is more reliable." This matches the provided answer.

Which of the following statements is TRUE about the weight placed on information in respect to its reliability?单项选择题

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