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Sequential Monte Carlo (SMC) methods are widely used to draw samples from intractable target distributions. Particle degeneracy can hinder the use of SMC when the target distribution is highly constrained or multimodal. As a motivating…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
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 machine learning, which frames all inference as…
We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…
The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance…
Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…
The preferential sampling of locations chosen to observe a spatio-temporal process has been identified as a major problem across multiple fields. Predictions of the process can be severely biased when standard statistical methodologies are…
Monte Carlo (MC) sampling algorithms are an extremely widely-used technique to estimate expectations of functions f(x), especially in high dimensions. Control variates are a very powerful technique to reduce the error of such estimates, but…
Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…
Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012)…
We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on $\mathbb{R}^d$ for large $d$. It is well known that using a single importance sampling step one produces…
Monte Carlo (MC) simulations of many systems, in particular those with conflicting constraints, can be considerably speeded up by using multicanonical or related methods. Some of these approaches sample with a-priori unknown weight factors.…
We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient,…
We present the MCscales approach for incorporating scale uncertainties in parton distribution functions (PDFs). The new methodology builds on the Monte Carlo sampling for propagating experimental uncertainties into the PDF space that…
Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…
Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows…
We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for…