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In this paper approximation methods for infinite-dimensional Levy processes, also called (time-dependent) Levy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional…
We propose a new generator for the generalized inverse Gaussian (GIG) distribution by decomposing the density of GIG into two components. The first component is a truncated inverse Gamma density, in order to sample from which we improve the…
A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of non-equilibrium systems. Results for the quasi-stationary probability distribution in two model systems are compared with the…
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…
Adaptive importance sampling (AIS) methods provide a useful alternative to Markov Chain Monte Carlo (MCMC) algorithms for performing inference of intractable distributions. Population Monte Carlo (PMC) algorithms constitute a family of AIS…
Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
Gaussian Boson Sampling (GBS) have shown advantages over classical methods for performing some specific sampling tasks. To fully harness the computational power of GBS, there has been great interest in identifying their practical…
In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…
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…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…
The self-learning Metropolis-Hastings algorithm is a powerful Monte Carlo method that, with the help of machine learning, adaptively generates an easy-to-sample probability distribution for approximating a given hard-to-sample distribution.…