  A random-walk Metropolis sampler is geometrically ergodic if its equilibrium
density is super-exponentially light and satisfies a curvature condition
[Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including
Bayesian analysis with conjugate priors of logistic and Poisson regression and
of log-linear models for categorical data result in posterior distributions
that are not super-exponentially light. We show how to apply the
change-of-variable formula for diffeomorphisms to obtain new densities that do
satisfy the conditions for geometric ergodicity. Sampling the new variable and
mapping the results back to the old gives a geometrically ergodic sampler for
the original variable. This method of obtaining geometric ergodicity has very
wide applicability.
