Let ₁,...,, iid from N(u, o2) where o² is known. (a) Show that the Jeffreys prior for the normal likelihood is n(u) = C₁√n/0², μER for some constant c₁ > 0. (b) Is this a proper prior or improrer prior? Explain. (c) Derive the posterior density for u under the normal likelihood N(μ, o) and Jeffreys prior for u. Plot the density. (d) Simulate 1,000 draws from the posterior derived in (c) and plot a histogram of the simulated values. (e) Let = exp(μ). Find the posterior density of analytically and plot the density. (f) Estimate by Monte Carlo integration. (g) Compute a 95% equal tail interval for analytically and by simulation.
Let ₁,...,, iid from N(u, o2) where o² is known. (a) Show that the Jeffreys prior for the normal likelihood is n(u) = C₁√n/0², μER for some constant c₁ > 0. (b) Is this a proper prior or improrer prior? Explain. (c) Derive the posterior density for u under the normal likelihood N(μ, o) and Jeffreys prior for u. Plot the density. (d) Simulate 1,000 draws from the posterior derived in (c) and plot a histogram of the simulated values. (e) Let = exp(μ). Find the posterior density of analytically and plot the density. (f) Estimate by Monte Carlo integration. (g) Compute a 95% equal tail interval for analytically and by simulation.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:Let x₁,...,x, iid from N(u, o2) where o² is known.
(a) Show that the Jeffreys prior for the normal likelihood is
n(u) = c₁√n/0², MER
for some constant c₁ > 0.
(b) Is this a proper prior or improrer prior? Explain.
(c) Derive the posterior density for u under the normal likelihood N(μ, o) and Jeffreys
prior for u. Plot the density.
(d) Simulate 1,000 draws from the posterior derived in (c) and plot a histogram of the
simulated values.
(e) Let 0 = exp(u). Find the posterior density of analytically and plot the density.
(f) Estimate by Monte Carlo integration.
(g) Compute a 95% equal tail interval for analytically and by simulation.
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VIEWStep 3: Check whether the given prior probability for μ is a proper prior or improper prior and Explain
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