Related papers: Fast Bayesian Multilevel Quasi-Monte Carlo
This article introduces a Bayesian neural network estimation method for quantile regression assuming an asymmetric Laplace distribution (ALD) for the response variable. It is shown that the posterior distribution for feedforward neural…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use…
Recent developments in big data and analytics research have produced an abundance of large data sets that are too big to be analyzed in their entirety, due to limits on computer memory or storage capacity. To address these issues,…
Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established…
The efficient approximation of quantity of interest derived from PDEs with lognormal diffusivity is a central challenge in uncertainty quantification. In this study, we propose a multilevel quasi-Monte Carlo framework to approximate…
Convolutional neural network (CNN) has achieved unprecedented success in image super-resolution tasks in recent years. However, the network's performance depends on the distribution of the training sets and degrades on out-of-distribution…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
Practical structural engineering problems are often characterized by significant uncertainties. Historically, one of the prevalent methods to account for this uncertainty has been the standard Monte Carlo (MC) method. Recently, improved…
Machine learning models, and deep neural networks in particular, are increasingly deployed in risk-sensitive domains such as healthcare, environmental forecasting, and finance, where reliable quantification of predictive uncertainty is…
In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
Methods for generating sequences of surrogates approximating fine scale models of two-phase random heterogeneous media are presented that are designed to adaptively control the modeling error in key quantities of interest (QoIs). For…
Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schr\"odinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of $N_w$ walkers, making…
Gaussian and discrete non-Gaussian spatial datasets are common across fields like public health, ecology, geosciences, and social sciences. Bayesian spatial generalized linear mixed models (SGLMMs) are a flexible class of models for…
Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…
Approximate Bayesian computation (ABC) is a class of Bayesian inference algorithms that targets for problems with intractable or {unavailable} likelihood function. It uses synthetic data drawn from the simulation model to approximate the…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
We explore the application of the quasi-Monte Carlo (QMC) method in deep backward dynamic programming (DBDP) (Hure et al. 2020) for numerically solving high-dimensional nonlinear partial differential equations (PDEs). Our study focuses on…