Bernstein–von Mises theorem (Q4894580)

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theorem that the posterior converges in the infinite-data limit 𝑁≫1 to a multivariate normal distribution centred at the maximum likelihood estimator with covariance 𝑁⁻¹𝐼(𝜃₀)⁻¹ with 𝜃₀ the true population parameter and 𝐼(𝜃₀) the Fisher information
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Bernstein–von Mises theorem
theorem that the posterior converges in the infinite-data limit 𝑁≫1 to a multivariate normal distribution centred at the maximum likelihood estimator with covariance 𝑁⁻¹𝐼(𝜃₀)⁻¹ with 𝜃₀ the true population parameter and 𝐼(𝜃₀) the Fisher information

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