Related papers: Hamiltonian Monte Carlo Methods for Subset Simulat…
Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…
The Hawkes process is a widely used model in many areas, such as finance, seismology, neuroscience, epidemiology, and social sciences. Estimation of the Hawkes process from continuous observations of a sample path is relatively…
We propose a generic approach for numerically efficient simulation from analytically intractable distributions with constrained support. Our approach relies upon Generalized Randomized Hamiltonian Monte Carlo (GRHMC) processes and combines…
Terrorist activities often exhibit temporal and spatial clustering, making the multivariate Hawkes process (MHP) a useful statistical model for analysing terrorism across different geographic regions. However, terror attack data from the…
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…
Hamiltonian Monte Carlo (HMC) improves the computational efficiency of the Metropolis algorithm by reducing its random walk behavior. Riemannian Manifold HMC (RMHMC) further improves HMC's performance by exploiting the geometric properties…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
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,…
The coalescence of binary neutron stars are one of the main sources of gravitational waves for ground-based gravitational wave detectors. As Bayesian inference for binary neutron stars is computationally expensive, more efficient and faster…
Sequential Monte Carlo (SMC) algorithms represent a suite of robust computational methodologies utilized for state estimation and parameter inference within dynamical systems, particularly in real-time or online environments where data…
Dynamically rescaled Hamiltonian Monte Carlo (DRHMC) is introduced as a computationally fast and easily implemented method for performing full Bayesian analysis in hierarchical statistical models. The method relies on introducing a modified…
In this paper, we propose Barrier Hamiltonian Monte Carlo (BHMC), a version of the HMC algorithm which aims at sampling from a Gibbs distribution $\pi$ on a manifold $\mathrm{M}$, endowed with a Hessian metric $\mathfrak{g}$ derived from a…
We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
Markov Chain Monte Carlo (MCMC) is an invaluable means of inference with complicated models, and Hamiltonian Monte Carlo, in particular Riemannian Manifold Hamiltonian Monte Carlo (RMHMC), has demonstrated impressive success in many…
In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in…
Splitting schemes are numerical integrators for Hamiltonian problems that may advantageously replace the St\"ormer-Verlet method within Hamiltonian Monte Carlo (HMC) methodology. However, HMC performance is very sensitive to the step size…
The Bouncy Particle Sampler is a Markov chain Monte Carlo method based on a nonreversible piecewise deterministic Markov process. In this scheme, a particle explores the state space of interest by evolving according to a linear dynamics…
Markov chain Monte Carlo methods such as Gibbs sampling and simple forms of the Metropolis algorithm typically move about the distribution being sampled via a random walk. For the complex, high-dimensional distributions commonly encountered…
Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are state-of-the-art methods for taking samples from high-dimensional distributions with a differentiable density function. To generate samples, they numerically integrate…