An inverse Gaussian distribution with mean and variance has the ƒ (2₁A)=√xp{-12-2 (2-1)²} f(x;μ) density x > 0. (a) Determine 2 different Laplace approximations for μ. (b) Which one is better. Explain why.

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An inverse Gaussian distribution with mean μ and variance μ has the
density
P { - 12/2 (2-μ)²}
fl
f(x; μ) =
√2nx³
exp
x > 0.
(a) Determine 2 different Laplace approximations for μ.
(b) Which one is better. Explain why.
Transcribed Image Text:An inverse Gaussian distribution with mean μ and variance μ has the density P { - 12/2 (2-μ)²} fl f(x; μ) = √2nx³ exp x > 0. (a) Determine 2 different Laplace approximations for μ. (b) Which one is better. Explain why.
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