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We discuss convergence results of the Laplace approximation in terms of the Hellinger distance and analyze the efficiency of Monte Carlo methods based on it. In particular, we show that Laplace-based importance sampling and Laplace-based quasi-Monte-Carlo methods are robust w.r.t.\u00a0the concentration of the posterior for large classes of posterior distributions and integrands whereas prior-based importance sampling and plain quasi-Monte Carlo are not. Numerical experiments are presented to illustrate the theoretical findings.<\/jats:p>","DOI":"10.1007\/s00211-020-01131-1","type":"journal-article","created":{"date-parts":[[2020,7,13]],"date-time":"2020-07-13T12:07:27Z","timestamp":1594642047000},"page":"915-971","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":47,"title":["On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems"],"prefix":"10.1007","volume":"145","author":[{"given":"Claudia","family":"Schillings","sequence":"first","affiliation":[]},{"given":"Bj\u00f6rn","family":"Sprungk","sequence":"additional","affiliation":[]},{"given":"Philipp","family":"Wacker","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,13]]},"reference":[{"issue":"1","key":"1131_CR1","doi-asserted-by":"crossref","first-page":"A243","DOI":"10.1137\/140992564","volume":"38","author":"A Alexanderian","year":"2016","unstructured":"Alexanderian, A., Petra, N., Stadler, G., Ghattas, O.: A fast and scalable method for a-optimal design of experiments for infinite-dimensional Bayesian nonlinear inverse problems. 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