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[Normal approximation to posterior under generalized linear models] Suppose we have a random sample yi P oisson(i), i = 1, 2, . , n, where log(i) =...

[Normal approximation to posterior under generalized linear models] Suppose we have a random sample yi ∼ P oisson(λi), i = 1, 2, . . . , n, where log(λi) = (Xβ)i and X ∈ R n×n and β ∈ R p . Matrix X is known. However, coefficient β is unknown. Suppose n is large. Given a noninformative (i.e. uniform) prior, please derive the approximate multivariate normal distribution to the posterior at the posterior mode. You need to specify the man vector and variance-covariance matrix of this multivariate norma

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