Abstract
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.
Original language | English (US) |
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Pages (from-to) | 3050-3076 |
Number of pages | 27 |
Journal | Annals of Statistics |
Volume | 40 |
Issue number | 6 |
DOIs | |
State | Published - Dec 2012 |
Keywords
- Change of variable
- Conjugate prior
- Drift condition
- Exponential family
- Markov chain Monte Carlo
- Markov chain isomorphism
- Metropolis-Hastings-Green algorithm