Related papers: Magnetic Manifold Hamiltonian Monte Carlo
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic…
We propose a new Markov Chain Monte Carlo (MCMC) method for constrained target distributions. Our method first maps the $D$-dimensional constrained domain of parameters to the unit ball ${\bf B}_0^D(1)$. Then, it augments the resulting…
Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…
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…
We present a comprehensive comparison of different Markov Chain Monte Carlo (MCMC) sampling methods, evaluating their performance on both standard test problems and cosmological parameter estimation. Our analysis includes traditional…
We present the Monte Carlo with Absorbing Markov Chains (MCAMC) method for extremely long kinetic Monte Carlo simulations. The MCAMC algorithm does not modify the system dynamics. It is extremely useful for models with discrete state spaces…
Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…
Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions.…
Riemann manifold Hamiltonian Monte Carlo (RMHMC) has the potential to produce high-quality Markov chain Monte Carlo-output even for very challenging target distributions. To this end, a symmetric positive definite scaling matrix for RMHMC,…
Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated,…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Particle Markov Chain Monte Carlo (PMCMC) is a general computational approach to Bayesian inference for general state space models. Our article scales up PMCMC in terms of the number of observations and parameters by generating the…
Manifold Markov chain Monte Carlo algorithms have been introduced to sample more effectively from challenging target densities exhibiting multiple modes or strong correlations. Such algorithms exploit the local geometry of the parameter…
We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
We consider conditional tests for non-negative discrete exponential families. We develop two Markov Chain Monte Carlo (MCMC) algorithms which allow us to sample from the conditional space and to perform approximated tests. The first…
We develop Microcanonical Hamiltonian Monte Carlo (MCHMC), a class of models which follow a fixed energy Hamiltonian dynamics, in contrast to Hamiltonian Monte Carlo (HMC), which follows canonical distribution with different energy levels.…
There has been considerable interest in designing Markov chain Monte Carlo algorithms by exploiting numerical methods for Langevin dynamics, which includes Hamiltonian dynamics as a deterministic case. A prominent approach is Hamiltonian…
The main purpose of this paper is to facilitate the communication between the Analytic, Probabilistic and Algorithmic communities. We present a proof of convergence of the Hamiltonian (Hybrid) Monte Carlo algorithm from the point of view of…