Related papers: Sampling approach to sparse approximation problem:…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
We consider a problem of model selection in high-dimensional binary Markov random fields. The usefulness of the Ising model in studying systems of complex interactions has been confirmed in many papers. The main drawback of this model is…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
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…
The Stochastic Approximation EM (SAEM) algorithm, a variant stochastic approximation of EM, is a versatile tool for inference in incomplete data models. In this paper, we review the fundamental EM algorithm and then focus especially on the…
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…
Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from…
In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to Holder data in general bounded domains of $\mathbb{R}^d$. We aim at two fundamental goals. The first, and the most…
This paper concerns a high-dimensional stochastic programming problem of minimizing a function of expected cost with a matrix argument. To this problem, one of the most widely applied solution paradigms is the sample average approximation…
Sampling a diverse set of high-quality solutions for hard optimization problems is of great practical relevance in many scientific disciplines and applications, such as artificial intelligence and operations research. One of the main open…
Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…
Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose…
The efficient simulation of the mean value of a non-linear functional of the solution to a linear stochastic partial differential equation (SPDE) with additive Gaussian noise is considered. A Galerkin finite element method is employed along…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
In this paper we propose the approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance…
Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…
Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad…