Related papers: Probabilistic Path Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a popular sampling method in Bayesian inference. Recently, Heng & Jacob (2019) studied Metropolis HMC with couplings for unbiased Monte Carlo estimation, establishing a generic parallelizable scheme for HMC.…

Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…

Zigzag and other piecewise deterministic Markov process samplers have attracted significant interest for their non-reversibility and other appealing properties for Bayesian posterior computation. Hamiltonian Monte Carlo is another…

Hamiltonian Monte Carlo is a powerful algorithm for sampling from difficult-to-normalize posterior distributions. However, when the geometry of the posterior is unfavorable, it may take many expensive evaluations of the target distribution…

Hamiltonian Flow Monte Carlo(HFMC) methods have been implemented in engineering, biology and chemistry. HFMC makes large gradient based steps to rapidly explore the state space. The application of the Hamiltonian dynamics allows to estimate…

We establish the geometric ergodicity of the preconditioned Hamiltonian Monte Carlo (HMC) algorithm defined on an infinite-dimensional Hilbert space, as developed in [Beskos et al., Stochastic Process. Appl., 2011]. This algorithm can be…

We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family…

Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though…

We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities where classical HMC is not an option due to intractable gradients, KMC adaptively learns…

Markov Chain Monte Carlo (MCMC) is a flexible approach to approximate sampling from intractable probability distributions, with a rich theoretical foundation and comprising a wealth of exemplar algorithms. While the qualitative correctness…

Bayesian inference methods such as Markov Chain Monte Carlo (MCMC) typically require repeated computations of the likelihood function, but in some scenarios this is infeasible and alternative methods are needed. Simulation-based inference…

Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…

Recently, it has been shown that the hybrid Monte Carlo (HMC) algorithm is guaranteed to converge exponentially to a given target probability distribution $p(x)\propto e^{-V(x)}$ on non-compact spaces if augmented by an appropriate radial…

There is a lack of methodological results to design efficient Markov chain Monte Carlo (MCMC) algorithms for statistical models with discrete-valued high-dimensional parameters. Motivated by this consideration, we propose a simple framework…

Phylogenetic comparative methods correct for shared evolutionary history among a set of non-independent organisms by modeling sample traits as arising from a diffusion process along on the branches of a possibly unknown history. To…

Riemannian manifold Hamiltonian Monte Carlo (RMHMC) is a powerful method of Bayesian inference that exploits underlying geometric information of the posterior distribution in order to efficiently traverse the parameter space. However, the…

Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…

Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is…

Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…