Related papers: Multilevel Monte Carlo simulation of a diffusion w…
This position paper summarizes a recently developed research program focused on inference in the context of data centric science and engineering applications, and forecasts its trajectory forward over the next decade. Often one endeavours…
We consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by Brownian motions in the commonly occurring small noise regime. We consider (i) standard Monte Carlo methods combined…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
We develop a scalable multi-step Monte Carlo algorithm for inference under a large class of nonparametric Bayesian models for clustering and classification. Each step is "embarrassingly parallel" and can be implemented using the same Markov…
Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great…
Motivated by a challenging problem in financial trading we are presented with a mixture of regressions with variable selection problem. In this regard, one is faced with data which possess outliers, skewness and, simultaneously, due to the…
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the…
In this work, we present, analyze, and implement a class of Multi-Level Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis-Hastings proposals for Bayesian inverse problems. In this context, the likelihood function…
Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…
Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…
We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, such as high-frequency…
In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model…
The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower…
This paper proposes a Sequential Monte Carlo approach for the Bayesian estimation of mixed causal and noncausal models. Unlike previous Bayesian estimation methods developed for these models, Sequential Monte Carlo offers extensive…
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…
In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…
We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…