4 papers · 1 filter
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…
Implications of weak convergence rates of Markov transition kernels
Austin Brown
This article extends weak convergence bounds of Markov transition kernels to convergence bounds on the variance of the Markov kernel applied to Lipschitz functions. In the reversib…
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…