IAI Actuarial Core Principles · Actuarial Statistics · Bayesian inference: priors, posteriors, loss functions and credible intervals
The posterior distribution of a mean μ is Normal with mean 52 and variance 16. What is the equal-tailed 95% Bayesian credible interval for μ? (Use z = 1.96.)
The interval is (44.16, 59.84). The posterior standard deviation is 4, the square root of the variance 16, so the interval is 52 plus or minus 1.96 times 4, which is 7.84. Using the variance instead of the standard deviation would be wrong.
- A(44.16, 59.84)Correct
- B(50.04, 53.96)
- C(36.32, 67.68)
- D(48.08, 55.92)
- (20.64, 83.36)
Explanation
The posterior standard deviation is √16 = 4. The interval is 52 ± 1.96×4 = 52 ± 7.84, giving (44.16, 59.84). Using the variance 16 in place of the standard deviation gives 52 ± 31.36, which is (20.64, 83.36) and is wrong.
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