Related papers: Bayesian analysis of hierarchical multi-fidelity c…

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…

We propose a data-efficient Gaussian process-based Bayesian approach to the semi-supervised learning problem on graphs. The proposed model shows extremely competitive performance when compared to the state-of-the-art graph neural networks…

Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modelling technique for approximating expensive computational models. However, it tends to get impractical for high-dimensional problems due to the size of the inherent…

We propose a novel Bayesian nonparametric method for hierarchical modelling on a set of related density functions, where grouped data in the form of samples from each density function are available. Borrowing strength across the groups is a…

When computer codes are used for modeling complex physical systems, their unknown parameters are tuned by calibration techniques. A discrepancy function may be added to the computer code in order to capture its discrepancy with the real…

Motivation: A branching processes model yields an unevenly stochastically distributed dataset that consists of sparse and dense regions. This work addresses the problem of precisely evaluating parameters for such a model. Applying a…

We consider the problem of calibrating an imperfect computer model using experimental data. To compensate the misspecification of the computer model and make more accurate predictions, a discrepancy function is often included and modeled…

Bayesian optimization has emerged as a highly effective tool for the safe online optimization of systems, due to its high sample efficiency and noise robustness. To further enhance its efficiency, reduced physical models of the system can…

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the…

Sequential Bayesian Filtering aims to estimate the current state distribution of a Hidden Markov Model, given the past observations. The problem is well-known to be intractable for most application domains, except in notable cases such as…

Thanks to computing power increase, the certification and the conception of complex systems relies more and more on simulation. To this end, predictive codes are needed, which have generally to be evaluated in a huge number of input points.…

We classify two types of Hierarchical Bayesian Model found in the literature as Hierarchical Prior Model (HPM) and Hierarchical Stochastic Model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

The computational efficiency of approximate Bayesian computation (ABC) has been improved by using surrogate models such as Gaussian processes (GP). In one such promising framework the discrepancy between the simulated and observed data is…

Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…