Related papers: Weak error for nested Multilevel Monte Carlo

If the conclusion of a data analysis is sensitive to dropping very few data points, that conclusion might hinge on the particular data at hand rather than representing a more broadly applicable truth. How could we check whether this…

For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles2015) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin…

In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

It is widely known that the performance of Markov chain Monte Carlo (MCMC) can degrade quickly when targeting computationally expensive posterior distributions, such as when the sample size is large. This has motivated the search for MCMC…

In this paper we establish mixed weak inequalities of Fefferman-Stein type for Calder\'on-Zygmund operators and their commutators, improving some previous results known in the literature. The main estimates also generalize the classical…

We propose and analyze a Multilevel Richardson-Romberg (MLRR) estimator which combines the higher order bias cancellation of the Multistep Richardson-Romberg method introduced in [Pa07] and the variance control resulting from the…

We consider a class of M-estimators of the parameters of a GARCH (p,q) model. These estimators involve score functions and, for adequate choices of the score functions, are asymptotically normal under milder moment assumptions than the…

High statistical precision is critical for Monte Carlo (MC) samples in high energy physics and is degraded by negatively weighted events. This paper investigates a procedure to learn the relationship between the negative and positive weight…

Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an…

Average calibration of the (variance-based) prediction uncertainties of machine learning regression tasks can be tested in two ways: one is to estimate the calibration error (CE) as the difference between the mean absolute error (MSE) and…

Nested integration of the form $\int f\left(\int g(\bs{y},\bs{x})\di{}\bs{x}\right)\di{}\bs{y}$, characterized by an outer integral connected to an inner integral through a nonlinear function $f$, is a challenging problem in various fields,…

We consider geothermal inverse problems and uncertainty quantification from a Bayesian perspective. Our main goal is to make standard, `out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models by…

We assume a drift condition towards a small set and bound the mean square error of estimators obtained by taking averages along a single trajectory of a Markov chain Monte Carlo algorithm. We use these bounds to construct fixed-width…

This paper studies the rate of convergence for conditional quasi-Monte Carlo (QMC), which is a counterpart of conditional Monte Carlo. We focus on discontinuous integrands defined on the whole of $R^d$, which can be unbounded. Under…

We construct an efficient estimator for the error distribution function of the nonparametric regression model Y = r(Z) + e. Our estimator is a kernel smoothed empirical distribution function based on residuals from an under-smoothed local…

In this article, we consider weighted weak type $(1,1)$ inequality for certain square function associated to differences of ball averages and martingale in the non-commutative setting. This establishes a weighted version of main result of…

The problem whether weighted estimates for multilinear Fourier multipliers with Sobolev regularity hold under weak condition on weights is considered.

We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…

We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…