Related papers: Efficient Bayesian Sampling with Langevin Birth-De…
We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. Such settings have recently drawn considerable interest in the context of generative modelling…
In this article, we focus on the sampling of the configurational Gibbs-Boltzmann distribution, that is, the calculation of averages of functions of the position coordinates of a molecular $N$-body system modelled at constant temperature. We…
Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…
Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
Modeling non-Markovian time series is a recent topic of research in many fields such as climate modeling, biophysics, molecular dynamics, or finance. The generalized Langevin equation (GLE), given naturally by the Mori-Zwanzig projection…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
Bayesian model selection provides a powerful and mathematically transparent framework to tackle hypothesis testing, such as detection tests of gravitational waves emitted during the coalescence of binary systems using ground-based laser…
We study the design and implementation of numerical methods to solve the generalized Langevin equation (GLE) focusing on canonical sampling properties of numerical integrators. For this purpose, we cast the GLE in an extended phase space…
A Bayesian approach is developed for the inference of an eddy-diffusivity field from Lagrangian trajectory data. The motion of Lagrangian particles is modelled by a stochastic differential equation associated with the advection-diffusion…
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…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…
This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…
Priors with non-smooth log-densities, such as the l1-prior, are widely used in Bayesian inverse problems for their sparsity-inducing properties. Existing Langevin-based sampling methods typically rely on proximal mappings or smooth…
Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…
Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…
The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…