Let x1, . . . , xn iid from N(µ, σ^2 ) where σ^2 = 1. (a) Show that the Jeffreys prior for the normal likelihood is p(µ) = c1 √n/σ^2 , µ ∈ R for some constant c1 > 0. (b) Is this a proper prior or improrer prior? Explain.
Let x1, . . . , xn iid from N(µ, σ^2 ) where σ^2 = 1. (a) Show that the Jeffreys prior for the normal likelihood is p(µ) = c1 √n/σ^2 , µ ∈ R for some constant c1 > 0. (b) Is this a proper prior or improrer prior? Explain.
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 30E
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Let x1, . . . , xn iid from N(µ, σ^2 ) where σ^2 = 1. (a) Show that the Jeffreys prior for the normal likelihood is p(µ) = c1 √n/σ^2 , µ ∈ R for some constant c1 > 0. (b) Is this a proper prior or improrer prior? Explain.
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Step 1: Given information
VIEWStep 2: Calculate likelihood and log-likelihood function.
VIEWStep 3: Calculate first derivation of the log-likelihood function
VIEWStep 4: Calculate second derivative
VIEWStep 5: Calculate Fisher's Information function and Jeffery's prior.
VIEWStep 6: Determine Jeffery prior is proper or improper.
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