Related papers: Particle MCMC for Bayesian Microwave Control
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…
We investigate the use of the Metropolis-Hastings algorithm to sample posterior distribution in a Bayesian inverse problem, where the likelihood function is random. Concretely, we consider the case where one has full field observations of a…
We consider state and parameter estimation in multiple target tracking problems with data association uncertainties and unknown number of targets. We show how the problem can be recast into a conditionally linear Gaussian state-space model…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
We revise the basic concepts beneath the idea of \textit{superparamagnetism} and the suitability of Monte Carlo (MC) simulations to study superparamagnetic (SPM) properties. Starting with the description of the characteristic features of…
In the following article we develop a particle filter for approximating Feynman-Kac models with indicator potentials. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models…
Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest…
Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…
Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or…
Integration over non-negative integrands is a central problem in machine learning (e.g. for model averaging, (hyper-)parameter marginalisation, and computing posterior predictive distributions). Bayesian Quadrature is a probabilistic…
Efficient sampling of many-dimensional and multimodal density functions is a task of great interest in many research fields. We describe an algorithm that allows parallelizing inherently serial Markov chain Monte Carlo (MCMC) sampling by…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
Marginalization techniques are presented for the Bayesian filtering problem under the assumption of Gaussian priors and posteriors and a set of sequentially more constraining state space model assumptions. The techniques provide the…
Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the…
Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability…
Radial velocity (RV) planet searches are increasingly finding planets with small velocity amplitudes, with long orbital periods, or in multiple planet systems. Bayesian inference has the potential to improve the interpretation of existing…
Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on time-invariant deterioration model parameters either within an…
The general applicability and ease of use of the pseudo-marginal Metropolis--Hastings (PMMH) algorithm, and particle Metropolis--Hastings in particular, makes it a popular method for inference on discretely observed Markovian stochastic…
We present a parameter estimation procedure based on a Bayesian framework by applying a Markov Chain Monte Carlo algorithm to the calibration of the dynamical parameters of a space based gravitational wave detector. The method is based on…
Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases…