Mathematics · Bayesian Inference
Suppose X1, X2, ..., Xn are independent and identically distributed N(0, τ-2) random variables, where τ-2 > 0. Let the prior distribution on τ2 have density π(τ2) ∝ (1/τ2)α for some α > 0. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The posterior distribution is improper for α = 1.
- 2Under a squared error loss, the generalized Bayes estimator of τ2 is n/2 - α∑ Xi2 / 2.
- 3The posterior distribution is a proper distribution for all α > 0.
- 4The prior distribution is an improper distribution for all α > 0.✓
Correct answer
The prior distribution is an improper distribution for all α > 0.
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