This web site goes with a paper and an R contributed package.

## Paper

Leif T. Johnson and Charles J. Geyer (2012)

Google Inc. and University of Minnesota

Variable Transformation to Obtain Geometric Ergodicity in the Random-walk Metropolis Algorithm

Annals of Statistics,40, 3050–3076Leif T. Johnson and Charles J. Geyer (2013)

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

Annals of Statistics,41, 2698

**Abstract**

A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition (Jarner and Hansen, 2000). 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.

Here is the text of the paper (PDF).

Once sentence of the paper is in error. A correction has been accepted by
the *Annals of Statistics*.

Here is the text of the correction (PDF).

## Package

As the paper says the methods of the paper are easily implemented using
the R contributed package `mcmc`

, which is
CRAN contributed package.

Version 0.9 of the package, which is on CRAN now, has a new function
`morph.metrop`

which implements the methodology of the paper
in a foolproof

way, where foolproof

means there is nothing
the user can screw up (and does **not** mean that it somehow
magically makes MCMC give correct answers from ridiculously short runs).
This function is illustrated in
a
new package vignette (which is a PDF file).