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\\ ==== Prochaine séance ====
[[seminaires:StatP6P7:index|Séminaire de statistique]]\\
Mardi 24 mars 2026, 10 heures 45, Jussieu en salle Emile Borel 15-16-209\\
**Mikołaj Kasprzak** (ESSEC) //Quality of the Laplace approximation of Bayesian posteriors and cut posteriors.//
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The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using rate-of-convergence bounds from certain versions of the Bayesian Central Limit Theorem (BCLT) to provide quality guarantees. But existing bounds require assumptions that are unrealistic even for relatively simple real-life Bayesian analyses; more specifically, existing bounds either (1) require knowing the true data-generating parameter, (2) are asymptotic in the number of samples, (3) do not control the Bayesian posterior mean, or (4) require strongly log concave models to compute. I will present the first computable bounds on quality that simultaneously (1) do not require knowing the true parameter, (2) apply to finite samples, (3) control posterior means and variances, and (4) apply generally to models that satisfy the conditions of the asymptotic BCLT.  The bounds I will present substantially improve the dimension dependence of existing bounds; in fact, they achieve the lowest-order dimension dependence possible in the general case. In the second part of the talk, I will discuss very recent results regarding the quality of the Laplace approximation of cut posteriors, which are widely used in Bayesian modular inference. This is based on joint work with Ryan Giordano and Tamara Broderick and a recent project with Emilia Pompe and Pierre Jacob.
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