Related papers: Batch simulations and uncertainty quantification i…
Approximate Bayesian computation (ABC) have become a essential tool for the analysis of complex stochastic models. Earlier, Grelaud et al. (2009) advocated the use of ABC for Bayesian model choice in the specific case of Gibbs random…
Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference…
Bayesian optimization (BO) is a popular method for black-box optimization, which relies on uncertainty as part of its decision-making process when deciding which experiment to perform next. However, not much work has addressed the effect of…
We develop a Gaussian process ("GP") framework for modeling mortality rates and mortality improvement factors. GP regression is a nonparametric, data-driven approach for determining the spatial dependence in mortality rates and jointly…
Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…
Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
The Gaussian process (GP) is a Bayesian nonparametric paradigm that is widely adopted for uncertainty quantification (UQ) in a number of safety-critical applications, including robotics, healthcare, as well as surveillance. The consistency…
We present an approach for satisfying state constraints in systems with nonparametric uncertainty by estimating this uncertainty with a real-time-update Gaussian process (GP) model. Notably, new data is incorporated into the model in real…
Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…
Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…
This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…
Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable…
Approximate Bayesian computation (ABC) is one of the most popular "likelihood-free" methods. These methods have been applied in a wide range of fields by providing solutions to intractable likelihood problems in which exact Bayesian…
Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…
Bayesian inference provides a principled framework for probabilistic reasoning. If inference is performed in two steps, uncertainty propagation plays a crucial role in accounting for all sources of uncertainty and variability. This becomes…
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…
Uncertainty Quantification (UQ) is receiving more and more attention for engineering applications in particular from robust optimization. Indeed, running a computer experiment only provides a limited knowledge in terms of uncertainty and…
Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…
Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide…