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One of the well-known challenges in optimal experimental design is how to efficiently estimate the nested integrations of the expected information gain. The Gaussian approximation and associated importance sampling have been shown to be…
This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…
Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte…
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…
Many geosciences data are imprecise due to various limitations and uncertainties in the measuring process. One way to preserve this imprecision in a geostatistical mapping framework is to characterize the measurements as intervals rather…
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…
We use approximate Bayesian computation (ABC) combined with an "improved" Markov chain Monte Carlo (IMCMC) method to estimate posterior distributions of model parameters in subgrid-scale (SGS) closures for large eddy simulations (LES) of…
Stochastic kriging is a popular technique for simulation metamodeling due to its exibility and analytical tractability. Its computational bottleneck is the inversion of a covariance matrix, which takes $O(n^3)$ time in general and becomes…
We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of…
Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial differential equations (PDEs), they are computationally…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…
The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…
We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell…
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…
Accept-reject based Markov chain Monte Carlo (MCMC) methods are the workhorse algorithm for Bayesian inference. These algorithms, like Metropolis-Hastings, require choosing a proposal distribution which is typically informed by the desired…
Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions.…