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Bayesian methods are critical for quantifying the behaviors of systems. They capture our uncertainty about a system's behavior using probability distributions and update this understanding as new information becomes available. Probabilistic…
This report proposes a novel framework for a rigorous robustness analysis of stochastic biochemical systems. The technique is based on probabilistic model checking. We adapt the general definition of robustness introduced by Kitano to the…
We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…
Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a…
Neural network (NN) potentials promise highly accurate molecular dynamics (MD) simulations within the computational complexity of classical MD force fields. However, when applied outside their training domain, NN potential predictions can…
We propose a novel Markov chain Monte-Carlo (MCMC) method for reverse engineering the topological structure of stochastic reaction networks, a notoriously challenging problem that is relevant in many modern areas of research, like…
In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems. It is based on the generalized multiscale finite element method (GMsFEM) and multilevel…
Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution $\pi$ defined on a space $(\Theta,\mathcal{T})$ consist of the simulation of realisations of Markov chains $\{\theta_{n},n\geq1\}$ of invariant distribution…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
Amid growing interest in machine learning, numerous data-driven models have recently been developed for Reynolds-averaged turbulence modelling. However, their results generally show that they do not give accurate predictions for test cases…
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters.…
Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from…
Markov chain Monte Carlo (MCMC) is a simulation method commonly used for estimating expectations with respect to a given distribution. We consider estimating the covariance matrix of the asymptotic multivariate normal distribution of a…
This study is a first step towards using data-informed differential models to predict and control the dynamics of cancer-on-chip experiments. We consider a conceptualized one-dimensional device, containing a cancer and a population of white…
Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the…
Hamiltonian Monte Carlo (HMC) has emerged as a powerful Markov Chain Monte Carlo (MCMC) method to sample from complex continuous distributions. However, a fundamental limitation of HMC is that it can not be applied to distributions with…
Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised…
Machine learning (ML) offers promising new approaches to tackle complex problems and has been increasingly adopted in chemical and materials sciences. Broadly speaking, ML models employ generic mathematical functions and attempt to learn…
Inference after model selection presents computational challenges when dealing with intractable conditional distributions. Markov chain Monte Carlo (MCMC) is a common method for sampling from these distributions, but its slow convergence…
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…