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Assume Y₁,..., Ynud Normal(u, o2) where o2 is fixed and the unknown mean μ has prior ~ Normal(0, 0²/m). (a) Give a 95% posterior interval for µ. (b) Select a value of m and argue that for this choice your' 95% posterior credible interval has frequentist coverage 0.95 (that is, if you draw many samples of size n and compute the 95% interval following the formula in (a) for each sample, in the long-run 95% of the intervals will contain the true value of μ).

Assume Y₁,..., Ynud Normal(u, o2) where o2 is fixed and the unknown mean μ has prior ~ Normal(0, 0²/m). (a) Give a 95% posterior interval for µ. (b) Select a value of m and argue that for this choice your' 95% posterior credible interval has frequentist coverage 0.95 (that is, if you draw many samples of size n and compute the 95% interval following the formula in (a) for each sample, in the long-run 95% of the intervals will contain the true value of μ).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 7E
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1. Assume Y₁,..., Ynu id Normal(µ, o²) where o² is fixed and the Normal(0, 0²/m). unknown mean μ has prior μ~ н (a) Give a 95% posterior interval for µ. (b) Select a value of m and argue that for this choice your' 95% posterior credible interval has frequentist coverage 0.95 (that is, if you draw many samples of size n and compute the 95% interval following the formula in (a) for each sample, in the long-run 95% of the intervals will contain the true value of µ).
Transcribed Image Text:1. Assume Y₁,..., Ynu id Normal(µ, o²) where o² is fixed and the Normal(0, 0²/m). unknown mean μ has prior μ~ н (a) Give a 95% posterior interval for µ. (b) Select a value of m and argue that for this choice your' 95% posterior credible interval has frequentist coverage 0.95 (that is, if you draw many samples of size n and compute the 95% interval following the formula in (a) for each sample, in the long-run 95% of the intervals will contain the true value of µ).
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