4 papers
Markov Chain CLTs: Resolving Open Problems
Austin Brown, Jeffrey S. Rosenthal, Quan Zhou
Markov chain central limit theorems (CLTs) and their associated variances are very important for implementing Markov chain Monte Carlo algorithms among other applications. Häggströ…
Hyper-V uniform ergodicity of Markov chains
Austin Brown, Kshitij Khare
We develop a new uniform drift condition and local minorization that implies a stronger weighted form of uniform ergodicity for Markov chains we call hyper-V uniform ergodicity. Th…
Upper and lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo
Austin Brown, Jeffrey S. Rosenthal
We investigate lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo under any adaptation strategy. In particular, we prove general lower bounds in tota…
Weak convergence of adaptive Markov chain Monte Carlo
Austin Brown, Jeffrey S. Rosenthal
This article develops general conditions for weak convergence of adaptive Markov chain Monte Carlo processes and is shown to imply a weak law of large numbers for bounded Lipschitz…