arXiv subjects

Sabrina Sixta

Publications and source records attributed to Sabrina Sixta.

3 recordsLinked to original sources

arXiv2023

Estimating MCMC convergence rates using common random number simulation

This paper presents how to use common random number (CRN) simulation to evaluate Markov chain Monte Carlo (MCMC) convergence to stationarity. We provide an upper bound on the Wasserstein distance of a Markov chain to its stationary distribution after $N$ steps in terms of averages over CRN simulations. We apply our bound to Gibbs samplers on a model related to James-Stein estimators, a variance component model, and a Bayesian linear regression model. Using our examples, we show that the CRN-based simulation combined with a coalescing condition to generate a total variation bound converges to zero much more faster than the available drift and minorization bounds, while also converging at the same rate as the one-shot coupling bound.

stat.CO↗

arXiv2022

Convergence rate bounds for iterative random functions using one-shot coupling

One-shot coupling is a method of bounding the convergence rate between two copies of a Markov chain in total variation distance, which was first introduced by Roberts and Rosenthal and generalized by Madras and Sezer. The method is divided into two parts: the contraction phase, when the chains converge in expected distance and the coalescing phase, which occurs at the last iteration, when there is an attempt to couple. One-shot coupling does not require the use of any exogenous variables like a drift function or a minorization constant. In this paper, we summarize the one-shot coupling method into the One-Shot Coupling Theorem. We then apply the theorem to two families of Markov chains: the random functional autoregressive process and the autoregressive conditional heteroscedastic (ARCH) process. We provide multiple examples of how the theorem can be used on various models including ones in high dimensions. These examples illustrate how the theorem's conditions can be verified in a straightforward way. The one-shot coupling method appears to generate tight geometric convergence rate bounds.

stat.CO↗

arXiv2021

On Some Problems of Confidence Region Construction

The general problem of constructing confidence regions is unsolved in the sense that there is no algorithm that provides such a region with guaranteed coverage for an arbitrary parameter $ψ\inΨ.$ Moreover, even when such a region exists, it may be absurd in the sense that either the set $Ψ$ or the null set $ϕ$ is reported with positive probability. An approach to the construction of such regions with guaranteed coverage and which avoids absurdity is applied here to several problems that have been discussed in the recent literature and for which some standard approaches produce absurd regions.

math.ST↗