## 32 Citations

### Hamiltonian Monte Carlo Without Detailed Balance

- PhysicsICML
- 2014

A method for performing Hamiltonian Monte Carlo that largely eliminates sample rejection for typical hyperparameters and significantly suppresses the random walk behavior and wasted function evaluations that are typically the consequence of update rejection is presented.

### Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions

- MathematicsArXiv
- 2021

A delayed rejection variant of Hamiltonian Monte Carlo that makes one or more subsequent proposals each using a step size geometrically smaller than the last if an initial HMC trajectory is rejected, providing increased robustness to step size misspecification.

### Identifying the Optimal Integration Time in Hamiltonian Monte Carlo

- Physics
- 2016

By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided that the algorithm…

### Modified Hamiltonian Monte Carlo for Bayesian inference

- Computer ScienceStat. Comput.
- 2020

It is shown that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible part of the dynamics into a chain, and is called Mix & Match Hamiltonian Monte Carlo (MMHMC).

### Hamiltonian Monte Carlo with explicit, reversible, and volume-preserving adaptive step size control

- PhysicsJSIAM Lett.
- 2017

A new explicit, reversible, and volume-preserving integration method is proposed to adaptively set the step sizes, which does not violate the detailed balance condition or require a large increase in computational time.

### A Markov Jump Process for More Efficient Hamiltonian Monte Carlo

- Mathematics
- 2015

In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be…

### Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models.

- Computer Science
- 2020

This work presents dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type and uses a particlewise coupling that is contractive in a complementary particlewise metric.

### Geometry and Dynamics for Markov Chain Monte Carlo

- MathematicsArXiv
- 2017

The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners, and other users of the methodology with only a basic understanding of Monte Carlo methods.

### On the geometric ergodicity of Hamiltonian Monte Carlo

- MathematicsBernoulli
- 2019

We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both…

### HMC: Reducing the number of rejections by not using leapfrog and some results on the acceptance rate

- Computer ScienceJ. Comput. Phys.
- 2021

## References

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- Computer ScienceStatistics in medicine
- 1999

Some of the issues in developing adaptive methods for Markov chain Monte Carlo methods are outlined and some preliminary results are presented.

### Hamiltonian Monte Carlo Without Detailed Balance

- PhysicsICML
- 2014

A method for performing Hamiltonian Monte Carlo that largely eliminates sample rejection for typical hyperparameters and significantly suppresses the random walk behavior and wasted function evaluations that are typically the consequence of update rejection is presented.

### Practical Markov Chain Monte Carlo

- Mathematics
- 1992

The case is made for basing all inference on one long run of the Markov chain and estimating the Monte Carlo error by standard nonparametric methods well-known in the time-series and operations research literature.

### Optimum Monte-Carlo sampling using Markov chains

- Mathematics
- 1973

SUMMARY The sampling method proposed by Metropolis et al. (1953) requires the simulation of a Markov chain with a specified 7i as its stationary distribution. Hastings (1970) outlined a general…

### Compressible generalized hybrid Monte Carlo.

- Computer ScienceThe Journal of chemical physics
- 2014

This work presents a general framework for constructing hybrid Monte Carlo methods under relaxed conditions: the only geometric property needed is (weakened) reversibility; volume preservation is not needed.

### Delayed rejection in reversible jump Metropolis–Hastings

- Business
- 2001

SUMMARY In a Metropolis-Hastings algorithm, rejection of proposed moves is an intrinsic part of ensuring that the chain converges to the intended target distribution. However, persistent rejection,…

### Optimal tuning of the hybrid Monte Carlo algorithm

- Computer Science
- 2010

It is proved that, to obtain an O(1) acceptance probability as the dimension d of the state space tends to, the leapfrog step-size h should be scaled as h=l ×d−1/ 4, which means that in high dimensions, HMC requires O(d1/ 4 ) steps to traverse the statespace.

### Markov Chain Monte Carlo and Numerical Differential Equations

- Mathematics
- 2014

The aim of this contribution is to provide a readable account of Markov Chain Monte Carlo methods, with particular emphasis on their relations with the numerical integration of deterministic and…