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The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…
This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
Controlled branching processes are stochastic growth population models in which the number of individuals with reproductive capacity in each generation is controlled by a random control function. The purpose of this work is to examine the…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
We present a new approach to sample from generic binary distributions, based on an exact Hamiltonian Monte Carlo algorithm applied to a piecewise continuous augmentation of the binary distribution of interest. An extension of this idea to…
Rich data generating mechanisms are ubiquitous in this age of information and require complex statistical models to draw meaningful inference. While Bayesian analysis has seen enormous development in the last 30 years, benefitting from the…
Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…
Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…
Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model, and…
Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…
We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139--1160], showing how algorithms which are approximations to an…
We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…
Equality-constrained models naturally arise in problems in which measurements are taken at different levels of resolution. The challenge in this setting is that the models usually induce a joint distribution which is intractable. Resorting…
This paper focuses on variational inference with intractable likelihood functions that can be unbiasedly estimated. A flexible variational approximation based on Gaussian mixtures is developed, by adopting the mixture population Monte Carlo…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational…
We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global…