Variance bounding Markov chains.

By Gareth O. Roberts, Jeffrey S. Rosenthal. 2008

63 citations recorded by the source corpus.

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, vari- ance bounding is equivalent to the existence of usual central limit theorems for all L 2 functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Peskun order. We close with some applications to Metropolis-Hastings algorithms.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cbb0657c4ba28b2898c8917fb2ad54e15ac68a40

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (2012, background): “some cases the existence of a uniformupperbound ¯wis indeed necessary. The above results are statements on the (right) spectral gap of P˜ only, which is equivalent to variance bounding property of P˜ [31]. In some applications, geometric ergodicity may be more desirable than variance boundedness. We”
Convergence rates for a class of estimators based on Stein’s method (2016, background): “ntical to Eqn. 12 up to the inclusion of a factor 0 <˛<1 and a factor 1=N. Arguing as in Lemma 2 with C~ dreplaced by ˛N 1 C~ dcompletes the proof. Proof of Theorem 2. We appeal to Theorem 1 of Roberts and Rosenthal (2008). This states that reversible, geometrically ergodic Markov chains fx ig”