This paper reviews the mathematical foundation of the importance sampling technique and
discusses two general classes of methods to construct the importance sampling density (or …

We review adaptive Markov chain Monte Carlo algorithms (MCMC) as a mean to optimise
their performance. Using simple toy examples we review their theoretical underpinnings …

Summary Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as
the two main tools to sample from high dimensional probability distributions. Although …

The purpose of this book is to provide a self-contained entry into Monte Carlo computational
techniques. First and foremost, it must not be confused with a programming addendum to …

Statistical signal processing applications usually require the estimation of some parameters
of interest given a set of observed data. These estimates are typically obtained either by …

Sequential techniques can enhance the efficiency of the approximate Bayesian computation
algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is …

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

This book is a graduate-level introduction to probabilistic programming. It not only provides a
thorough background for anyone wishing to use a probabilistic programming system, but …

Uncertainty quantification (UQ) includes the characterization, integration, and propagation of
uncertainties that result from stochastic variations and a lack of knowledge or data in the …

Bayesian inference provides a consistent method for the extraction of information from
physics experiments even in ill-conditioned circumstances. The approach provides a unified …