Particle filters contain the promise of fully nonlinear data assimilation. They have been
applied in numerous science areas, including the geosciences, but their application to high …

ABSTRACT Statisticians often use Monte Carlo methods to approximate probability
distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential …

A central research challenge for the mathematical sciences in the twenty-first century is the
development of principled methodologies for the seamless integration of (often vast) data …

A fundamental problem in signal processing is the estimation of unknown parameters or
functions from noisy observations. Important examples include localization of objects in …

Approximate Bayesian computation (ABC) is a popular approach to address inference
problems where the likelihood function is intractable, or expensive to calculate. To improve …

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical
machines, can find application in many fields, from physics to chemistry. We introduce the …

Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …

The basic idea of importance sampling is to use independent samples from a proposal
measure in order to approximate expectations with respect to a target measure. It is key to …

This paper provides a unifying mean field based framework for the derivation and analysis of
ensemble Kalman methods. Both state estimation and parameter estimation problems are …

A core problem in statistics and probabilistic machine learning is to compute probability
distributions and expectations. This is the fundamental problem of Bayesian statistics and …