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Quasi Monte Carlo and multilevel Monte Carlo methods for computing posterior expectations in elliptic inverse problems

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Figure

Figure 1: Convergence w.r.t. h|right), respectively. The dotted and dashed reference slopes areE of the discretisation errors |Qh/Zh − Q2h/Z2h|, |Qh − Q2h| andZh−Z2h| (top left), as well as convergence w.r.t
Figure 2: Computational cost of ratio estimators Q�h/Z �h to achieve a RMSE e(Q �h/Z �h) of ε, usingthe same random samples in Q�h and in Z�h (left) and using different random samples in Q�h and inZ�h (right), respectively.
Figure 3: Sampling errors E[(Q �h/Z �h − Qh/Zh)2]1/2 as a function of noise level σ2η (left) and as afunction of number of observations m (right), respectively.

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