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The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…
Gradient-based Markov Chain Monte Carlo methods have recently received much attention for sampling discrete distributions, with interesting connections to their continuous counterparts. For examples, there are two discrete analogues to the…
We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on…
In longitudinal data a response variable is measured over time, or under different conditions, for a cohort of individuals. In many situations all intended measurements are not available which results in missing values. If the missing value…
Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM), though they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on…
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…
Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet, fitting these models to partially observed data is a notoriously difficult task due to intractability of the…
Likelihood-free inference methods based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. When applied in the context of any latent variable…
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…
Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo method with the appealing feature of being amenable to parallel computing. At each iteration, it samples several candidates for the next state of the Markov chain and…
Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present…
There has been considerable interest in designing Markov chain Monte Carlo algorithms by exploiting numerical methods for Langevin dynamics, which includes Hamiltonian dynamics as a deterministic case. A prominent approach is Hamiltonian…
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…
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…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
We construct an adaptive independent Metropolis-Hastings sampler that uses a mixture of normals as a proposal distribution. To take full advantage of the potential of adaptive sampling our algorithm updates the mixture of normals…
The classical Metropolis-Hastings (MH) algorithm can be extended to generate non-reversible Markov chains. This is achieved by means of a modification of the acceptance probability, using the notion of vorticity matrix. The resulting Markov…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
In this paper we introduce a new sampling algorithm which has the potential to be adopted as a universal replacement to the Metropolis--Hastings algorithm. It is related to the slice sampler, and motivated by an algorithm which is…
While recent work has shown that scores from models trained by the ubiquitous masked language modeling (MLM) objective effectively discriminate probable from improbable sequences, it is still an open question if these MLMs specify a…