  The Metropolis-Hastings method is often used to construct a Markov chain with
a given $\pi$ as its stationary distribution. The method works even if $\pi$ is
known only up to an intractable constant of proportionality. Polynomial time
convergence results for such chains (rapid mixing) are hard to obtain for high
dimensional probability models where the size of the state space potentially
grows exponentially with the model dimension. In a Bayesian context, Yang,
Wainwright, and Jordan (2016) (=YWJ) used the path method to prove rapid mixing
for high dimensional linear models. This paper proposes a modification of the
YWJ approach that simplifies the theoretical argument and improves the rate of
convergence. The new approach is illustrated by an application to an
exponentially weighted aggregation estimator.
