# Ordering, Slicing And Splitting Monte Carlo Markov Chains

@inproceedings{Mira1998OrderingSA, title={Ordering, Slicing And Splitting Monte Carlo Markov Chains}, author={Antonietta Mira}, year={1998} }

Markov chain Monte Carlo is a method of approximating the integral of a function f with respect to a distribution . A Markov chain that has as its stationary distribution is simulated producing samplesX1; X2; : : : . The integral is approximated by taking the average of f(Xn) over the sample path. The standard way to construct such Markov chains is the Metropolis-Hastings algorithm. The class P of all Markov chains having as their unique stationary distribution is very large, so it is important…

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## 23 Citations

### On the use of auxiliary variables inMarkov chain

- Mathematics
- 2007

We study the slice sampler, a method of constructing a reversible Markov chain with a speciied invariant distribution. Given an independence Metropolis-Hastings algorithm it is always possible to…

### Slice Sampling

- MathematicsThe Annals of Statistics
- 2003

Markov chain sampling methods that adapt to characteristics of the distribution being sampled can be constructed using the principle that one can ample from a distribution by sampling uniformly from…

### Efficiency and Convergence Properties of Slice Samplers

- Mathematics
- 2002

The slice sampler (SS) is a method of constructing a reversible Markov chain with a specified invariant distribution. Given an independence Metropolis–Hastings algorithm (IMHA) it is always possible…

### Limit theorems for sequential MCMC methods

- Mathematics, Computer ScienceAdvances in Applied Probability
- 2020

An $\mathbb{L}_r$ -inequality (which implies a strong law of large numbers) and a central limit theorem for sequential MCMC methods are established and conditions under which errors can be controlled uniformly in time are provided.

### LOCAL WEAK CONSISTENCY OF MARKOV CHAIN MONTE CARLO METHODS WITH APPLICATION TO MIXTURE MODEL

- Mathematics
- 2013

Markov chain Monte Calro methods (MCMC) are commonly used in Bayesian statistics. In the last twenty years, many results have been established for the calculation of the exact convergence rate of…

### On extended state-space constructions for Monte Carlo methods

- Computer Science
- 2015

A generic importance-sampling framework is described which admits virtually all Monte Carlo methods, including smc and mcmc methods, as special cases and hierarchical combinations of different Monte Carlo schemes can be justified as repeated applications of this framework.

### CONVERGENCE RATE OF MARKOV CHAINS ON

- Mathematics
- 2007

Acknowledgments. This work is part of my doctoral research done under the direction of Jeerey S. Rosenthal. I thank Peter Rosenthal for helpful discussions about the operator theory issues. Abstract.…

### Towards Automatic Reversible Jump Markov Chain Monte Carlo

- Computer Science
- 2005

The automatic sampler that is introduced in the penultimate chapter of the thesis builds upon the first steps taken by Green (2003) and uses adaptive techniques to perform self-tuning and calibration for many trans-dimensional statistical problems.

### Delayed Rejection in Reversible

- Business
- 1999

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, perhaps…

### 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.

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