Corrigendum to : Bounds on regeneration times and convergence rates for Markov chains

By G. O. Roberts, R. Tweedie. 2001

80 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b50ea75b108e35f56d300c2193915811bab5df2a

How researchers see this paper

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

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

On the geometric ergodicity of hybrid samplers (2003, background): “Explicit expressions for the rate r and for the constant R as a function of the terms in (2) and (3) can be found in [13], [11], [20], [18], [6], [3] and [4].”
Sufficient burn-in for Gibbs samplers for a hierarchical random effects model (2004, unknown): “THEOREM 3.2 [Roberts and Tweedie (1999, 2001)].”
Locally contracting iterated functions and stability of Markov chains (2001, background): “Under this condition, there is a more direct proof which also gives us quantitative bounds on the rate of convergence to stationarity similar to those in [11], [10] and [9].”
Optimal Proposal Distributions and Adaptive MCMC (2008, background): “This definition concerns distributional convergence (in total variation distance) as studied theoretically in e.g. Rosenthal (1995, 2002) and Roberts and Tweedie (1999).”
Geometric L 2 and L 1 convergence are equivalent for reversible Markov chains (2001, background): “…work on assessing when a Markov chain is geometrically ergodic (Chapters 15 and 16 of Meyn and Tweedie, 1993) and on the related problem of determining rates of convergence for geometrically ergodic chains (Meyn and Tweedie, 1994; Rosenthal, 1995: Lund and Tweedie, 1996; Roberts and Tweedie, 1999).”
Asymptotic Variance and Convergence Rates of Nearly-Periodic Markov Chain Monte Carlo Algorithms (2003, background): “For example, if Tn ¹ unif81121 : : : 1 n9, as opposed to Bn ¹ binomial42n1 1=25, then the distance of ¬4XTn5 to stationarity can be bounded using shift-coupling (Aldous and Thorisson 1993; Roberts and Rosenthal 1997a; Roberts and Tweedie 1999).”
Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms (2007, methodology): “It can be made somewhat more concrete using the theory of quantitative convergence rate bounds (see e.g. Meyn and Tweedie (1994), Rosenthal (1995), (2002), Roberts and Tweedie (1999), and Baxendale (2005)).”
General state space Markov chains and MCMC algorithms (2004, background): “And, how large is large enough?”
Geometric Ergodicity of van Dyk and Meng's Algorithm for the Multivariate Student's t Model (2004, methodology): “First, if geometric ergodicity is established through drift and minorization conditions, as it is here, then formulas like those of Rosenthal (1995) and Roberts and Tweedie (1999) can be used to calculate an appropriate burn-in before sampling begins.”