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This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…

In the presence of confounders, the ordinary least squares (OLS) estimator is known to be biased. This problem can be remedied by using the two-stage least squares (TSLS) estimator, based on the availability of valid instrumental variables…

Classical mixture models (MMs) are widely used tractable proposals for approximate inference settings such as variational inference (VI) and importance sampling (IS). Recently, mixture models with negative coefficients, called subtractive…

We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We…

Gaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate normal distribution, which arises from the discretisation of a…

Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…

A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…

The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…

Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…

Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods such as Markov chain Monte Carlo (MCMC) and importance sampling (IS). One such method is normalizing flows, which use a neural…

Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…

In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte…

This paper constructs an ensemble-based sampling smoother for four-dimensional data assimilation using a Hybrid/Hamiltonian Monte-Carlo approach. The smoother samples efficiently from the posterior probability density of the solution at the…

Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…

Sequential Monte Carlo (SMC), also known as particle filters, has been widely accepted as a powerful computational tool for making inference with dynamical systems. A key step in SMC is resampling, which plays the role of steering the…

We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…

Field level statistics, such as the minimum spanning tree (MST), have been shown to be a promising tool for parameter inference in cosmology. However, applications to real galaxy surveys are challenging, due to the presence of small scale…

This paper develops a novel sequential Monte Carlo (SMC) approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets. The approach…

Monte Carlo simulations using entropic sampling to estimate the number of configurations of a given energy are a valuable alternative to traditional methods. We introduce {\it tomographic} entropic sampling, a scheme which uses multiple…

Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal…