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Markov Chain Monte Carlo in Practice.
- Galin L. Jones, Qian Qin
- MathematicsAnnual review of public health
- 14 October 2021
TLDR
Geometric convergence bounds for Markov chains in Wasserstein distance based on generalized drift and contraction conditions
Let $\{X_n\}_{n=0}^\infty$ denote an ergodic Markov chain on a general state space that has stationary distribution $\pi$. This article concerns upper bounds on the $L_1$-Wasserstein distance between…
Estimating the spectral gap of a trace-class Markov operator
The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of the spectral gap of the corresponding Markov operator. However, calculating (and even approximating)…
Wasserstein-based methods for convergence complexity analysis of MCMC with applications
TLDR
Convergence complexity analysis of Albert and Chib’s algorithm for Bayesian probit regression
TLDR
On the limitations of single-step drift and minorization in Markov chain convergence analysis
TLDR
Asymptotically Stable Drift and Minorization for Markov Chains with Application to Albert and Chib's Algorithm
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Convergence Analysis of MCMC Algorithms for Bayesian Multivariate Linear Regression with Non‐Gaussian Errors
- J. Hobert, Yeun Ji Jung, K. Khare, Qian Qin
- Mathematics
- 1 September 2018
When Gaussian errors are inappropriate in a multivariate linear regression setting, it is often assumed that the errors are iid from a distribution that is a scale mixture of multivariate normals.…
Wasserstein-based methods for convergence complexity analysis of MCMC with application to Albert and Chib's algorithm
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