Multi-index Monte Carlo: when sparsity meets sampling

Multi-index Monte Carlo: when sparsity meets sampling

We propose and analyze a novel Multi Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the Multilevel Monte Carlo...

Compressed Sensing: “When sparsity meets sampling”∗

The recent theory of Compressed Sensing (Candès, Tao & Romberg, 2006, and Donoho, 2006) states that a signal, e.g. a sound record or an astronomical image, can be sampled at a rate much smaller than what is commonly prescribed by Shannon-Nyquist. The sampling of a signal can indeed be performed as a function of its “intrinsic dimension” rather than according to its cutoff frequency. This chapte...

Christiane Lemieux Monte Carlo and Quasi - Monte Carlo Sampling

Tomography Imaging Through the Monte Carlo Sampling

Efficient Monte Carlo sampling by parallel marginalization.

Markov chain Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper, a method is proposed to overcome this difficulty. The method utilizes information from rapidly equilibrating coarse Markov chains that sample marginal distributions of the full system. This is accomplished th...