Related papers: Geometry and Dynamics for Markov Chain Monte Carlo
Modern implementations of Hamiltonian Monte Carlo and related MCMC algorithms support sampling of probability functions that embed numerical root-finding algorithms, thereby allowing fitting of statistical models involving analytically…
We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by "splitting" the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
Markov chain Monte Carlo (MCMC) is widely regarded as one of the most important algorithms of the 20th century. Its guarantees of asymptotic convergence, stability, and estimator-variance bounds using only unnormalized probability functions…
In this paper we propose to evaluate and compare Markov chain Monte Carlo (MCMC) methods to estimate the parameters in a generalized extreme value model. We employed the Bayesian approach using traditional Metropolis-Hastings methods,…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
We present a method for performing Hamiltonian Monte Carlo that largely eliminates sample rejection for typical hyperparameters. In situations that would normally lead to rejection, instead a longer trajectory is computed until a new state…
The efficiency of Markov Chain Monte Carlo (MCMC) depends on how the underlying geometry of the problem is taken into account. For distributions with strongly varying curvature, Riemannian metrics help in efficient exploration of the target…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We…
We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
The shell model Monte Carlo (SMMC) method is a powerful technique for calculating the statistical and collective properties of nuclei in the presence of correlations in model spaces that are many orders of magnitude larger than those that…
Nonlinear systems of polynomial equations arise naturally in many applied settings, for example loglinear models on contingency tables and Gaussian graphical models. The solution sets to these systems over the reals are often positive…
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…
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,…
Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as…
We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…