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By the update formula𝜃 𝑡 =𝜃 𝑡−1 −𝛀 −1 𝑡 𝑔𝑡, we have 𝑉𝑡 = 𝛀1/2 𝑡 (𝜃 𝑡 −𝜃 ★) 2 2 = 𝛀1/2 𝑡 (𝜃 𝑡−1 −𝛀 −1 𝑡 𝑔𝑡 −𝜃 ★) 2 2 = 𝛀1/2 𝑡 (𝜃 𝑡−1 −𝜃 ★) 2 2 + 𝛀1/2 𝑡 𝛀−1 𝑡 𝑔𝑡 2 2 −2⟨𝛀 1/2 𝑡 (𝜃 𝑡−

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The Bernstein-von Mises theorem for Bayesian one-pass online learning

math.ST · 2026-04-30 · unverdicted · novelty 6.0

A one-pass Bayesian online learner with warm-start achieves optimal posterior convergence and satisfies an online Bernstein-von Mises theorem for uncertainty quantification.

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The Bernstein-von Mises theorem for Bayesian one-pass online learning math.ST · 2026-04-30 · unverdicted · none · ref 1
A one-pass Bayesian online learner with warm-start achieves optimal posterior convergence and satisfies an online Bernstein-von Mises theorem for uncertainty quantification.

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