Related papers: Particle filtering within adaptive Metropolis Hast…

In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution.…

Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at…

A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…

Likelihood-free methods such as approximate Bayesian computation (ABC) have extended the reach of statistical inference to problems with computationally intractable likelihoods. Such approaches perform well for small-to-moderate dimensional…

Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although the maximum composite likelihood estimator has frequentist properties akin to those of…

By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We…

Filtering in spatially-extended dynamical systems is a challenging problem with significant practical applications such as numerical weather prediction. Particle filters allow asymptotically consistent inference but require infeasibly large…

We present a scalable approach to performing approximate fully Bayesian inference in generic state space models. The proposed method is an alternative to particle MCMC that provides fully Bayesian inference of both the dynamic latent states…

We introduce a general framework that constructs estimators with reduced variance for random walk Metropolis and Metropolis-adjusted Langevin algorithms. The resulting estimators require negligible computational cost and are derived in a…

Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly concentrating target distributions. We focus on Gaussian…

Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…

Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional…

State space models (SSMs) are widely used to describe dynamic systems. However, when the likelihood of the observations is intractable, parameter inference for SSMs cannot be easily carried out using standard Markov chain Monte Carlo or…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

Particle filters are a group of algorithms to solve inverse problems through statistical Bayesian methods when the model does not comply with the linear and Gaussian hypothesis. Particle filters are used in domains like data assimilation,…

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable…

Several Bayesian estimation based heuristics have been developed to perform quantum state tomography (QST). Their ability to quantify uncertainties using region estimators and include a priori knowledge of the experimentalists makes this…

This paper is concerned with particle filtering for $\alpha$-stable stochastic volatility models. The $\alpha$-stable distribution provides a flexible framework for modeling asymmetry and heavy tails, which is useful when modeling financial…