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.