# Stereographic Markov Chain Monte Carlo

@inproceedings{Yang2022StereographicMC, title={Stereographic Markov Chain Monte Carlo}, author={Jun Yang and Krzysztof G. Latuszy'nski and Gareth O. Roberts}, year={2022} }

. High dimensional distributions, especially those with heavy tails, are notoriously diﬃcult for oﬀ the shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves, results in empirically observed ”stickiness” and poor theoretical mixing properties – lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high dimensional problem in Euclidean space onto a sphere and remedy these notorious…

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## References

SHOWING 1-10 OF 42 REFERENCES

Dimension-independent Markov chain Monte Carlo on the sphere

- Mathematics, Computer ScienceArXiv
- 2021

Efficient Markov chain Monte Carlo methods are derived for approximate sampling of posteriors with respect to high-dimensional spheres with angular central Gaussian priors, which show dimension-independent efficiency in numerical experiments.

Convergence of Heavy‐tailed Monte Carlo Markov Chain Algorithms

- Mathematics, Computer Science
- 2007

The paper gives for the first time a theoretical justification for the common belief that heavy‐tailed proposal distributions improve convergence in the context of random‐walk Metropolis algorithms.

Exponential ergodicity of the bouncy particle sampler

- MathematicsThe Annals of Statistics
- 2019

Non-reversible Markov chain Monte Carlo schemes based on piecewise deterministic Markov processes have been recently introduced in applied probability, automatic control, physics and statistics.…

High-dimensional scaling limits of piecewise deterministic sampling algorithms

- Computer Science
- 2018

Scaling limits for bothiecewise deterministic Markov processes are determined and based on these scaling limits the performance of the two algorithms in high dimensions can be compared.

Geometric ergodicity of the Bouncy Particle Sampler

- MathematicsThe Annals of Applied Probability
- 2020

The Bouncy Particle Sampler (BPS) is a Monte Carlo Markov Chain algorithm to sample from a target density known up to a multiplicative constant. This method is based on a kinetic piecewise…

Hypocoercivity of piecewise deterministic Markov process-Monte Carlo

- MathematicsThe Annals of Applied Probability
- 2021

In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov Process Monte Carlo methods…

Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms

- Mathematics
- 1996

We develop results on geometric ergodicity of Markov chains and apply these and other recent results in Markov chain theory to multidimensional Hastings and Metropolis algorithms. For those based on…

Monte Carlo on Manifolds: Sampling Densities and Integrating Functions

- Computer Science, MathematicsCommunications on Pure and Applied Mathematics
- 2018

An MCMC sampler is given for probability distributions defined by unnormalized densities on manifolds in euclidean space defined by equality and inequality constraints and used to develop a multistage algorithm to compute integrals over such manifolds.

Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates

- MathematicsThe Annals of Applied Probability
- 2021

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…

The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method

- Mathematics, Computer Science
- 2015

An alternative scheme recently introduced in the physics literature where the target distribution is explored using a continuous-time nonreversible piecewise-deterministic Markov process is explored, and several computationally efficient implementations of this Markov chain Monte Carlo schemes are proposed.