2 citations · 3 across the 9 of their papers we have counts for
9 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…
A non-asymptotic error analysis for parallel Monte Carlo estimation from many short Markov chains
Austin Brown
Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of co…
Estimating MCMC convergence rates using common random number simulation
Sabrina Sixta, Jeffrey S. Rosenthal, Austin Brown
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 Wasse…
Lower bounds on the rate of convergence for accept-reject-based Markov chains in Wasserstein and total variation distances
Austin Brown, Galin L. Jones
To avoid poor empirical performance in Metropolis-Hastings and other accept-reject-based algorithms practitioners often tune them by trial and error. Lower bounds on the convergenc…
Geometric ergodicity of Gibbs samplers for Bayesian error-in-variable regression
Austin Brown
Multivariate Bayesian error-in-variable (EIV) linear regression is considered to account for additional additive Gaussian error in the features and response. A 3-variable determini…
Exact Convergence Analysis for Metropolis-Hastings Independence Samplers in Wasserstein Distances
Austin Brown, Galin L. Jones
Under mild assumptions, we show the exact convergence rate in total variation is also exact in weaker Wasserstein distances for the Metropolis-Hastings independence sampler. We dev…