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

Variable transformation to obtain geometric ergodicity in the random-walk Metropolis algorithm