Related papers: Quasi-Monte Carlo for partial differential equatio…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…

In this paper, we study estimation of nonlinear models with cross sectional data using two-step generalized estimating equations (GEE) in the quasi-maximum likelihood estimation (QMLE) framework. In the interest of improving efficiency, we…

In this article we consider parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable Levy process, which is observed at high frequency. In most cases of practical interest, the likelihood…

We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity…

The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate solutions via certain Monte Carlo simulations. The main results represent the upper bound of…

ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi- Monte Carlo) sequences. We show that the resulting ABC…

We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…

We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…

In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are…

Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…

Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…

We apply the sample average approximation (SAA) method to risk-neutral optimization problems governed by nonlinear partial differential equations (PDEs) with random inputs. We analyze the consistency of the SAA optimal values and SAA…

Importance sampling (IS) is valuable in reducing the variance of Monte Carlo sampling for many areas, including finance, rare event simulation, and Bayesian inference. It is natural and obvious to combine quasi-Monte Carlo (QMC) methods…

A natural Monte Carlo method to approximate conditional expectations in a probabilistic framework is justified by a general result inspired on the Besicovitch covering theorem on differentiation of measures. The method is specially useful…

Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations…

In this paper we propose a generalization of a class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter for long-range dependent multivariate time series. We generalize a known GSE-type estimator by…

Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC…

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…