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Abstract Details

Activity Number: 655
Type: Contributed
Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing
Abstract - #306106
Title: Variable Transformation to Obtain Geometric Ergodicity in the Random-Walk Metropolis Algorithm
Author(s): Leif Johnson*+
Companies: Google
Address: 1600 Amphitheatre Parkway, Mountain View, CA, 94043, United States
Keywords: Markov chain Monte Carlo ; change of variable ; exponential familty ; conjugate prior ; Markov chain isomorphism ; Metropolis-Hastings-Green algorithm
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.


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