Binned Multilevel Monte Carlo for Bayesian Inverse Problems with Large Data

2016 ◽  
pp. 511-519 ◽  
Author(s):  
Robert N. Gantner ◽  
Claudia Schillings ◽  
Christoph Schwab
Keyword(s):  
Monte Carlo ◽  
Inverse Problems ◽  
Large Data ◽  
Multilevel Monte Carlo ◽  
Bayesian Inverse Problems

scholarly journals Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian Inverse Problems

2016 ◽  
Vol 308 ◽  
pp. 81-101 ◽  
Author(s):  
Shiwei Lan ◽  
Tan Bui-Thanh ◽  
Mike Christie ◽  
Mark Girolami
Keyword(s):  
Monte Carlo ◽  
Inverse Problems ◽  
Monte Carlo Methods ◽  
Higher Order ◽  
Bayesian Inverse Problems ◽  
Higher Order Tensors

scholarly journals Multilevel Sequential2 Monte Carlo for Bayesian inverse problems

2018 ◽  
Vol 368 ◽  
pp. 154-178 ◽  
Author(s):  
Jonas Latz ◽  
Iason Papaioannou ◽  
Elisabeth Ullmann
Keyword(s):  
Monte Carlo ◽  
Inverse Problems ◽  
Bayesian Inverse Problems

scholarly journals Bayesian inverse problems with Monte Carlo forward models

2013 ◽  
Vol 7 (1) ◽  
pp. 81-105 ◽  
Author(s):  
Guillaume Bal ◽  
◽  
Ian Langmore ◽  
Youssef Marzouk ◽  
Keyword(s):  
Monte Carlo ◽  
Inverse Problems ◽  
Forward Models ◽  
Bayesian Inverse Problems

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

scholarly journals Sequential ensemble transform for Bayesian inverse problems

2021 ◽  
Vol 427 ◽  
pp. 110055
Author(s):  
Aaron Myers ◽  
Alexandre H. Thiéry ◽  
Kainan Wang ◽  
Tan Bui-Thanh
Keyword(s):  
Inverse Problems ◽  
Bayesian Inverse Problems ◽  
Ensemble Transform

scholarly journals Space-time multilevel Monte Carlo methods and their application to cardiac electrophysiology

2021 ◽  
Vol 433 ◽  
pp. 110164
Author(s):  
S. Ben Bader ◽  
P. Benedusi ◽  
A. Quaglino ◽  
P. Zulian ◽  
R. Krause
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Cardiac Electrophysiology ◽  
Space Time ◽  
Multilevel Monte Carlo

scholarly journals Central limit theorem for the multilevel Monte Carlo Euler method

2015 ◽  
Vol 25 (1) ◽  
pp. 211-234 ◽  
Author(s):  
Mohamed Ben Alaya ◽  
Ahmed Kebaier
Keyword(s):  
Monte Carlo ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Euler Method ◽  
Multilevel Monte Carlo
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